{"id":"https://openalex.org/W2026669994","doi":"https://doi.org/10.1142/s0218127404011405","title":"NUMERICAL ANALYSIS OF DEGENERATE CONNECTING ORBITS FOR MAPS","display_name":"NUMERICAL ANALYSIS OF DEGENERATE CONNECTING ORBITS FOR MAPS","publication_year":2004,"publication_date":"2004-10-01","ids":{"openalex":"https://openalex.org/W2026669994","doi":"https://doi.org/10.1142/s0218127404011405","mag":"2026669994"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127404011405","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404011405","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110164030","display_name":"Wolf\u2010J\u00fcrgen Beyn","orcid":null},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"WOLF-J\u00dcRGEN BEYN","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062564873","display_name":"Thorsten H\u00fcls","orcid":null},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"THORSTEN H\u00dcLS","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016150299","display_name":"Yongkui Zou","orcid":"https://orcid.org/0000-0001-9519-1804"},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YONGKUI ZOU","raw_affiliation_strings":["Department of Mathematics, Jilin University, Changchun 130023, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jilin University, Changchun 130023, P. R. China","institution_ids":["https://openalex.org/I194450716"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7326,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.70364474,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"14","issue":"10","first_page":"3385","last_page":"3407"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980999827384949,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transversality","display_name":"Transversality","score":0.8857171535491943},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.8759610652923584},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.6977503299713135},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.6586254835128784},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5158595442771912},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4710930287837982},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36876749992370605},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3566972017288208},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3362467885017395},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20946037769317627},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.08960041403770447},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06498351693153381},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06223580241203308}],"concepts":[{"id":"https://openalex.org/C24167531","wikidata":"https://www.wikidata.org/wiki/Q2300767","display_name":"Transversality","level":2,"score":0.8857171535491943},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.8759610652923584},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.6977503299713135},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.6586254835128784},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5158595442771912},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4710930287837982},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36876749992370605},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3566972017288208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3362467885017395},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20946037769317627},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.08960041403770447},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06498351693153381},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06223580241203308}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127404011405","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404011405","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:pub.uni-bielefeld.de:1605465","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/1605465","pdf_url":null,"source":{"id":"https://openalex.org/S4306401671","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Beyn W-J, H\u00fcls T, Kleinkauf JM, Zou Y. Numerical analysis of degenerate connecting orbits for maps. <em>International Journal of Bifurcation and Chaos</em>. 2004;14(10):3385-3407.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W14078166","https://openalex.org/W93760757","https://openalex.org/W126935648","https://openalex.org/W160832363","https://openalex.org/W201746522","https://openalex.org/W203532357","https://openalex.org/W355012799","https://openalex.org/W654547933","https://openalex.org/W1488048473","https://openalex.org/W1514578360","https://openalex.org/W1530314303","https://openalex.org/W1534004526","https://openalex.org/W1541770559","https://openalex.org/W1596300602","https://openalex.org/W1596321532","https://openalex.org/W1760551737","https://openalex.org/W1971808848","https://openalex.org/W1982449011","https://openalex.org/W1999585119","https://openalex.org/W2008995486","https://openalex.org/W2019833761","https://openalex.org/W2022664063","https://openalex.org/W2025890352","https://openalex.org/W2028296976","https://openalex.org/W2041957871","https://openalex.org/W2045774013","https://openalex.org/W2047389619","https://openalex.org/W2061154922","https://openalex.org/W2073686912","https://openalex.org/W2074204676","https://openalex.org/W2076394902","https://openalex.org/W2083533842","https://openalex.org/W2083922917","https://openalex.org/W2088986191","https://openalex.org/W2091314510","https://openalex.org/W2093427279","https://openalex.org/W2122591635","https://openalex.org/W2140758684","https://openalex.org/W2154420880","https://openalex.org/W2186590998","https://openalex.org/W2905382927","https://openalex.org/W2973869319","https://openalex.org/W3123094903","https://openalex.org/W4206651839","https://openalex.org/W4214727197","https://openalex.org/W4285719527","https://openalex.org/W4294967943","https://openalex.org/W4301491118"],"related_works":["https://openalex.org/W2045665826","https://openalex.org/W155037358","https://openalex.org/W4240610494","https://openalex.org/W3006004107","https://openalex.org/W2980627813","https://openalex.org/W2615244697","https://openalex.org/W125373334","https://openalex.org/W1535429593","https://openalex.org/W561816457","https://openalex.org/W237418930"],"abstract_inverted_index":{"This":[0],"paper":[1],"contains":[2],"a":[3],"survey":[4],"of":[5,30,61,75,81],"numerical":[6,69],"methods":[7,36,77],"for":[8],"connecting":[9,40],"orbits":[10,41],"in":[11,48],"discrete":[12],"dynamical":[13],"systems.":[14],"Special":[15],"emphasis":[16],"is":[17],"put":[18],"on":[19,53],"degenerate":[20,63],"cases":[21,64],"where":[22],"either":[23],"the":[24,39,54,62,73,76,79,82],"orbit":[25,44],"loses":[26,33],"transversality":[27],"or":[28],"one":[29],"its":[31],"endpoints":[32],"hyperbolicity.":[34],"Numerical":[35],"that":[37,71],"approximate":[38],"by":[42],"finite":[43],"sequences":[45],"are":[46,57],"described":[47],"detail":[49],"and":[50,68,78],"theoretical":[51],"results":[52,70],"error":[55,83],"analysis":[56],"provided.":[58],"For":[59],"most":[60],"we":[65],"present":[66],"examples":[67],"illustrate":[72],"applicability":[74],"validity":[80],"estimates.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":15},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}