{"id":"https://openalex.org/W2028617788","doi":"https://doi.org/10.1007/s10208-004-0163-9","title":"An Algorithmic Approach to Chain Recurrence","display_name":"An Algorithmic Approach to Chain Recurrence","publication_year":2005,"publication_date":"2005-11-01","ids":{"openalex":"https://openalex.org/W2028617788","doi":"https://doi.org/10.1007/s10208-004-0163-9","mag":"2028617788"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-004-0163-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-004-0163-9","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004040775","display_name":"William D. Kalies","orcid":"https://orcid.org/0000-0002-8228-3598"},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"W.D. Kalies","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33434, USA","Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33434, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33434, USA","institution_ids":["https://openalex.org/I63772739"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33434, USA#TAB#","institution_ids":["https://openalex.org/I63772739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049298090","display_name":"Konstantin Mischaikow","orcid":"https://orcid.org/0000-0003-2876-4558"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"K. Mischaikow","raw_affiliation_strings":["Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332, USA","Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta GA 30332, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109092368","display_name":"Robert Vandervorst","orcid":null},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"R.C.A.M. VanderVorst","raw_affiliation_strings":["Department of Mathematics, Vrije University Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands","Department of Mathematics, Vrije University Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vrije University Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I865915315"]},{"raw_affiliation_string":"Department of Mathematics, Vrije University Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands#TAB#","institution_ids":["https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004040775","https://openalex.org/A5049298090","https://openalex.org/A5109092368"],"corresponding_institution_ids":["https://openalex.org/I130701444","https://openalex.org/I63772739","https://openalex.org/I865915315","https://openalex.org/I887064364"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.9556,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.96184438,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"5","issue":"4","first_page":"409","last_page":"449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7340770959854126},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.681851327419281},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.582510769367218},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5229300260543823},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4479210674762726},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44071489572525024},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3638460040092468},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3318437933921814},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2622317671775818},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19838488101959229},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10502949357032776},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09081277251243591}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7340770959854126},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.681851327419281},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.582510769367218},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5229300260543823},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4479210674762726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44071489572525024},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3638460040092468},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3318437933921814},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2622317671775818},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19838488101959229},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10502949357032776},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09081277251243591},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":7,"locations":[{"id":"doi:10.1007/s10208-004-0163-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-004-0163-9","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:research.vu.nl:openaire_cris_publications/019dc3b1-e4e6-412a-9494-ba224a7c1a8a","is_oa":false,"landing_page_url":"https://research.vu.nl/en/publications/019dc3b1-e4e6-412a-9494-ba224a7c1a8a","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":"Kalies, W D, Mischaikow, K & van der Vorst, R C A M 2005, 'An algorithmic approach to chain recurrence', Foundations of Computational Mathematics, vol. 5, no. 4, pp. 409-449. https://doi.org/10.1007/s10208-004-0163-9","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.155.2624","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.155.2624","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.rutgers.edu/~mischaik/papers/focm1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.167.741","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.167.741","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.vu.nl/%7Evdvorst/PAPERS/KMV-focm.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.330.2150","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.2150","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.fau.edu/kalies/papers/chainrec.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.71.4407","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.4407","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.fau.edu/kalies/papers/aacr.pdf","raw_type":"text"},{"id":"pmh:oai:research.vu.nl:publications/019dc3b1-e4e6-412a-9494-ba224a7c1a8a","is_oa":false,"landing_page_url":"https://hdl.handle.net/1871.1/019dc3b1-e4e6-412a-9494-ba224a7c1a8a","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":"Kalies, W D, Mischaikow, K & van der Vorst, R C A M 2005, 'An algorithmic approach to chain recurrence', Foundations of Computational Mathematics, vol. 5, no. 4, pp. 409-449. https://doi.org/10.1007/s10208-004-0163-9","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W162901799","https://openalex.org/W1528630040","https://openalex.org/W1575974143","https://openalex.org/W1589876408","https://openalex.org/W1605526073","https://openalex.org/W1942928910","https://openalex.org/W1979499447","https://openalex.org/W2011095097","https://openalex.org/W2037091548","https://openalex.org/W2044502494","https://openalex.org/W2055707808","https://openalex.org/W2111474755","https://openalex.org/W2163239611","https://openalex.org/W2326057307","https://openalex.org/W2752885492","https://openalex.org/W3021722416","https://openalex.org/W3145128584"],"related_works":["https://openalex.org/W2143578351","https://openalex.org/W2025910816","https://openalex.org/W2333819912","https://openalex.org/W2321824256","https://openalex.org/W1995284689","https://openalex.org/W1987272770","https://openalex.org/W2947186315","https://openalex.org/W2019334017","https://openalex.org/W2170265659","https://openalex.org/W2078208578"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}