{"id":"https://openalex.org/W2077011938","doi":"https://doi.org/10.1142/s0218127405012533","title":"A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS","display_name":"A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS","publication_year":2005,"publication_date":"2005-03-01","ids":{"openalex":"https://openalex.org/W2077011938","doi":"https://doi.org/10.1142/s0218127405012533","mag":"2077011938"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405012533","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405012533","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/ws/files/2988488/2004r14.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072817844","display_name":"Bernd Krauskopf","orcid":"https://orcid.org/0000-0002-8940-230X"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"B. KRAUSKOPF","raw_affiliation_strings":["Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078314587","display_name":"Hinke M. Osinga","orcid":"https://orcid.org/0000-0003-2169-0883"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"H. M. OSINGA","raw_affiliation_strings":["Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK","Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK","institution_ids":["https://openalex.org/I36234482"]},{"raw_affiliation_string":"Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK#TAB#","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110309869","display_name":"Eusebius J. Doedel","orcid":null},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"E. J. DOEDEL","raw_affiliation_strings":["Department of Computer Science, Concordia University, 1455 Boulevard de Maisonneuve O., Montr\u00e9al Qu\u00e9bec, H3G 1M8, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Concordia University, 1455 Boulevard de Maisonneuve O., Montr\u00e9al Qu\u00e9bec, H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074592454","display_name":"Michael E. Henderson","orcid":"https://orcid.org/0009-0007-2206-0011"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. E. HENDERSON","raw_affiliation_strings":["IBM Research, PO Box 218, Yorktown Heights, NY 10598, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research, PO Box 218, Yorktown Heights, NY 10598, USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018563718","display_name":"John Guckenheimer","orcid":"https://orcid.org/0000-0001-6655-7862"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. GUCKENHEIMER","raw_affiliation_strings":["Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY 14853\u20134201, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY 14853\u20134201, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028818054","display_name":"Alexander Vladimirsky","orcid":"https://orcid.org/0000-0003-4284-4546"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. VLADIMIRSKY","raw_affiliation_strings":["Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY 14853\u20134201, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY 14853\u20134201, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079412932","display_name":"Michael Dellnitz","orcid":null},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. DELLNITZ","raw_affiliation_strings":["Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020280466","display_name":"Oliver Junge","orcid":"https://orcid.org/0000-0002-3435-307X"},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"O. JUNGE","raw_affiliation_strings":["Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5072817844"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":13.4642,"has_fulltext":true,"cited_by_count":267,"citation_normalized_percentile":{"value":0.9950103,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"15","issue":"03","first_page":"763","last_page":"791"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9873999953269958,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.8441163301467896},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.775198221206665},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.7243850231170654},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6100463271141052},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.5958421230316162},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.5808842778205872},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5651965737342834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5282995700836182},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.5072562098503113},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40418267250061035},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3338874578475952},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3305714428424835},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14498043060302734},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13882485032081604},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.13315048813819885},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13191473484039307},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12394171953201294},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.07393461465835571},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.061355024576187134},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.05696895718574524}],"concepts":[{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.8441163301467896},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.775198221206665},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.7243850231170654},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6100463271141052},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.5958421230316162},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.5808842778205872},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5651965737342834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5282995700836182},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.5072562098503113},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40418267250061035},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3338874578475952},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3305714428424835},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14498043060302734},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13882485032081604},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.13315048813819885},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13191473484039307},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12394171953201294},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.07393461465835571},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.061355024576187134},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.05696895718574524},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1142/s0218127405012533","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405012533","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/5b494aa8-2191-422d-8184-bda160c7cef4","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/5b494aa8-2191-422d-8184-bda160c7cef4","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Krauskopf, B, Osinga, HM, Doedel, EJ, Henderson, ME, Guckenheimer, JM, Vladimirsky, A, Dellnitz, M & Junge, O 2005, 'A survey of methods for computing (un)stable manifolds of vector fields', International Journal of Bifurcation and Chaos, vol. 15 (3), pp. 763 - 791. https://doi.org/10.1142/S0218127405012533","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research.vu.nl:publications/de697470-38c8-4c90-8565-fcd8bf1d6286","is_oa":false,"landing_page_url":"https://research.vu.nl/en/publications/de697470-38c8-4c90-8565-fcd8bf1d6286","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Krauskopf, B, Osinga, H M, Doedel, E J, Henderson, M E, Guckenheimer, J, Vladimirsky, A, Dellnitz, M & Junge, O 2005, 'A survey of method's for computing (un)stable manifold of vector fields', International Journal of Bifurcation and Chaos, vol. 15, no. 3, pp. 763-791. https://doi.org/10.1142/S0218127405012533","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/b3776aa9-5b72-453a-90a7-a133427ad6b1","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/b3776aa9-5b72-453a-90a7-a133427ad6b1","pdf_url":"https://research-information.bris.ac.uk/ws/files/2988488/2004r14.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Krauskopf, B, Osinga, HM, Doedel, EJ, Henderson, ME, Guckenheimer, J, Vladimirsky, A, Dellnitz, M & Junge, O 2004 'A survey of methods for computing (un)stable manifolds of vector fields'. < http://hdl.handle.net/1983/82 >","raw_type":"workingPaper"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/73b20629-790e-42ef-b740-d2185ead178a","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/73b20629-790e-42ef-b740-d2185ead178a","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Krauskopf, B, Osinga, HM, Doedel, EJ, Henderson, ME, Guckenheimer, J, Vladimirsky, A, Dellnitz, M & Junge, O 2006, A survey of methods for computing (un)stable manifolds of vector fields. in EJ Doedel, G Domokos & IG Kevrekidis (eds), Modeling and Computations in Dynamical Systems. vol. B13, World Scientific Series on Nonlinear Science, pp. 67 - 95.","raw_type":"bookPart"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/73b20629-790e-42ef-b740-d2185ead178a","is_oa":false,"landing_page_url":"https://research-information.bristol.ac.uk/en/publications/a-survey-of-methods-for-computing-unstable-manifolds-of-vector-fields(73b20629-790e-42ef-b740-d2185ead178a).html","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Krauskopf, B, Osinga, HM, Doedel, EJ, Henderson, ME, Guckenheimer, J, Vladimirsky, A, Dellnitz, M & Junge, O 2006, A survey of methods for computing (un)stable manifolds of vector fields. in EJ Doedel, G Domokos & IG Kevrekidis (eds), Modeling and Computations in Dynamical Systems. vol. B13, World Scientific Series on Nonlinear Science, pp. 67 - 95.","raw_type":"bookPart"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/b3776aa9-5b72-453a-90a7-a133427ad6b1","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:research.vu.nl:openaire_cris_publications/de697470-38c8-4c90-8565-fcd8bf1d6286","is_oa":false,"landing_page_url":"https://hdl.handle.net/1871.1/de697470-38c8-4c90-8565-fcd8bf1d6286","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Krauskopf, B, Osinga, H M, Doedel, E J, Henderson, M E, Guckenheimer, J, Vladimirsky, A, Dellnitz, M & Junge, O 2005, 'A survey of method's for computing (un)stable manifold of vector fields', International Journal of Bifurcation and Chaos, vol. 15, no. 3, pp. 763-791. https://doi.org/10.1142/S0218127405012533","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/b3776aa9-5b72-453a-90a7-a133427ad6b1","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/b3776aa9-5b72-453a-90a7-a133427ad6b1","pdf_url":"https://research-information.bris.ac.uk/ws/files/2988488/2004r14.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Krauskopf, B, Osinga, HM, Doedel, EJ, Henderson, ME, Guckenheimer, J, Vladimirsky, A, Dellnitz, M & Junge, O 2004 'A survey of methods for computing (un)stable manifolds of vector fields'. < http://hdl.handle.net/1983/82 >","raw_type":"workingPaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2077011938.pdf","grobid_xml":"https://content.openalex.org/works/W2077011938.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W61948969","https://openalex.org/W164995562","https://openalex.org/W977421267","https://openalex.org/W1249582468","https://openalex.org/W1500046813","https://openalex.org/W1501770280","https://openalex.org/W1568666422","https://openalex.org/W1571507625","https://openalex.org/W1575974143","https://openalex.org/W1589453449","https://openalex.org/W1596321532","https://openalex.org/W1650565123","https://openalex.org/W1876456565","https://openalex.org/W1971092129","https://openalex.org/W1978426466","https://openalex.org/W1983018211","https://openalex.org/W2001659478","https://openalex.org/W2006903827","https://openalex.org/W2009334861","https://openalex.org/W2012068782","https://openalex.org/W2013479853","https://openalex.org/W2016595627","https://openalex.org/W2021617431","https://openalex.org/W2026989737","https://openalex.org/W2027126956","https://openalex.org/W2027674062","https://openalex.org/W2041957871","https://openalex.org/W2048509006","https://openalex.org/W2049739431","https://openalex.org/W2055341194","https://openalex.org/W2062841339","https://openalex.org/W2071248198","https://openalex.org/W2071290058","https://openalex.org/W2072559684","https://openalex.org/W2077157707","https://openalex.org/W2079053578","https://openalex.org/W2079059625","https://openalex.org/W2083684282","https://openalex.org/W2089876099","https://openalex.org/W2094313519","https://openalex.org/W2110670499","https://openalex.org/W2141394518","https://openalex.org/W2164761951","https://openalex.org/W2316463358","https://openalex.org/W2478509250","https://openalex.org/W2485794283","https://openalex.org/W2574175061","https://openalex.org/W2618795383","https://openalex.org/W2739685101","https://openalex.org/W2905382927","https://openalex.org/W2922993169","https://openalex.org/W3144818527","https://openalex.org/W3168404227","https://openalex.org/W4206651839","https://openalex.org/W4230906466","https://openalex.org/W4255043459"],"related_works":["https://openalex.org/W2243875171","https://openalex.org/W2077011938","https://openalex.org/W3021060928","https://openalex.org/W2087723889","https://openalex.org/W1010944416","https://openalex.org/W3152370143","https://openalex.org/W1983459863","https://openalex.org/W2129195111","https://openalex.org/W1536954903","https://openalex.org/W2041496883"],"abstract_inverted_index":{"The":[0],"computation":[1],"of":[2,25,35,52],"global":[3,20],"invariant":[4],"manifolds":[5],"has":[6],"seen":[7],"renewed":[8],"interest":[9],"in":[10,55],"recent":[11],"years.":[12],"We":[13],"survey":[14],"different":[15],"approaches":[16],"for":[17],"computing":[18],"a":[19,26,36],"stable":[21,50],"or":[22],"unstable":[23],"manifold":[24,51],"vector":[27],"field,":[28],"where":[29],"we":[30],"concentrate":[31],"on":[32],"the":[33,44,48,53,56],"case":[34],"two-dimensional":[37,49],"manifold.":[38],"All":[39],"methods":[40],"are":[41],"illustrated":[42],"with":[43],"same":[45],"example":[46],"\u2014":[47],"origin":[54],"Lorenz":[57],"system.":[58]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":18},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":17}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}