{"id":"https://openalex.org/W1984401664","doi":"https://doi.org/10.1142/s0218127414500163","title":"Horseshoes, Entropy, Homoclinic Trajectories, and Lyapunov Stability","display_name":"Horseshoes, Entropy, Homoclinic Trajectories, and Lyapunov Stability","publication_year":2014,"publication_date":"2014-02-01","ids":{"openalex":"https://openalex.org/W1984401664","doi":"https://doi.org/10.1142/s0218127414500163","mag":"1984401664"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414500163","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500163","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/A5019721790","display_name":"Zden\u011bk Ko\u010dan","orcid":null},"institutions":[{"id":"https://openalex.org/I32366509","display_name":"Silesian University in Opava","ror":"https://ror.org/02w4f2z17","country_code":"CZ","type":"education","lineage":["https://openalex.org/I32366509"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Zden\u011bk Ko\u010dan","raw_affiliation_strings":["Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic","institution_ids":["https://openalex.org/I32366509"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083275108","display_name":"Veronika Kurkov\u00e1","orcid":null},"institutions":[{"id":"https://openalex.org/I32366509","display_name":"Silesian University in Opava","ror":"https://ror.org/02w4f2z17","country_code":"CZ","type":"education","lineage":["https://openalex.org/I32366509"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Veronika Kurkov\u00e1","raw_affiliation_strings":["Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic","institution_ids":["https://openalex.org/I32366509"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007775210","display_name":"Michal M\u00e1lek","orcid":"https://orcid.org/0000-0002-1893-8369"},"institutions":[{"id":"https://openalex.org/I32366509","display_name":"Silesian University in Opava","ror":"https://ror.org/02w4f2z17","country_code":"CZ","type":"education","lineage":["https://openalex.org/I32366509"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Michal M\u00e1lek","raw_affiliation_strings":["Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic","institution_ids":["https://openalex.org/I32366509"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I32366509"],"apc_list":null,"apc_paid":null,"fwci":0.4133,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.54366915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","issue":"02","first_page":"1450016","last_page":"1450016"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9990000128746033,"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":0.9990000128746033,"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/T12793","display_name":"Caveolin-1 and cellular processes","score":0.9386000037193298,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.9183183908462524},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9072504043579102},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7435984015464783},{"id":"https://openalex.org/keywords/hyperspace","display_name":"Hyperspace","score":0.529108464717865},{"id":"https://openalex.org/keywords/continuous-map","display_name":"Continuous map","score":0.5114661455154419},{"id":"https://openalex.org/keywords/topological-entropy-in-physics","display_name":"Topological entropy in physics","score":0.4559023082256317},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4552828073501587},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44182682037353516},{"id":"https://openalex.org/keywords/h\u00e9non-map","display_name":"H\u00e9non map","score":0.44178518652915955},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4374327063560486},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.35351431369781494},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.2158263623714447},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.18917694687843323},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1675911545753479},{"id":"https://openalex.org/keywords/topological-quantum-number","display_name":"Topological quantum number","score":0.11948356032371521},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11457511782646179},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.111630380153656},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07358938455581665}],"concepts":[{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.9183183908462524},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9072504043579102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7435984015464783},{"id":"https://openalex.org/C39368324","wikidata":"https://www.wikidata.org/wiki/Q5024959","display_name":"Hyperspace","level":2,"score":0.529108464717865},{"id":"https://openalex.org/C2991919592","wikidata":"https://www.wikidata.org/wiki/Q170058","display_name":"Continuous map","level":2,"score":0.5114661455154419},{"id":"https://openalex.org/C148908050","wikidata":"https://www.wikidata.org/wiki/Q11681505","display_name":"Topological entropy in physics","level":3,"score":0.4559023082256317},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4552828073501587},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44182682037353516},{"id":"https://openalex.org/C2781402108","wikidata":"https://www.wikidata.org/wiki/Q1642961","display_name":"H\u00e9non map","level":3,"score":0.44178518652915955},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4374327063560486},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35351431369781494},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.2158263623714447},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.18917694687843323},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1675911545753479},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.11948356032371521},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11457511782646179},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.111630380153656},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07358938455581665},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127414500163","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500163","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W207809827","https://openalex.org/W1568857594","https://openalex.org/W1569683457","https://openalex.org/W1968975267","https://openalex.org/W1986624435","https://openalex.org/W1994084768","https://openalex.org/W2015594477","https://openalex.org/W2024274666","https://openalex.org/W2050593189","https://openalex.org/W2053944816","https://openalex.org/W2095566293","https://openalex.org/W2122661929","https://openalex.org/W2156034977","https://openalex.org/W2157725729","https://openalex.org/W2318571547","https://openalex.org/W4252781609","https://openalex.org/W4253125818","https://openalex.org/W6854069325"],"related_works":["https://openalex.org/W3029997921","https://openalex.org/W4382199672","https://openalex.org/W4221161985","https://openalex.org/W4387788722","https://openalex.org/W4321351866","https://openalex.org/W2042690431","https://openalex.org/W2016490457","https://openalex.org/W1757250965","https://openalex.org/W2914185747","https://openalex.org/W2324262301"],"abstract_inverted_index":{"We":[0,100],"consider":[1],"six":[2],"properties":[3,40],"of":[4,11,17,22,32,46,67,72,79],"continuous":[5,86],"maps,":[6,48,69],"such":[7],"as":[8],"the":[9,15,20,30,38,44,65,70,77],"existence":[10,21,71],"an":[12,73,93],"arc":[13,74,94],"horseshoe,":[14],"positivity":[16,78],"topological":[18,80,98],"entropy,":[19,81],"a":[23,85,89],"homoclinic":[24],"trajectory,":[25],"or":[26],"Lyapunov":[27],"instability":[28],"on":[29,53,88],"set":[31],"periodic":[33],"points.":[34],"The":[35],"relations":[36],"between":[37],"considered":[39],"are":[41],"provided":[42],"in":[43,64],"case":[45,66],"graph":[47,68],"dendrite":[49],"maps":[50,52],"and":[51,96],"compact":[54],"metric":[55],"spaces.":[56],"For":[57],"example,":[58],"by":[59],"[Llibre":[60],"&":[61],"Misiurewicz,":[62],"1993]":[63],"horseshoe":[75,95],"implies":[76],"but":[82],"we":[83],"construct":[84],"map":[87],"Peano":[90],"continuum":[91],"with":[92],"zero":[97],"entropy.":[99],"also":[101],"formulate":[102],"one":[103],"open":[104],"problem.":[105]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
