{"id":"https://openalex.org/W2034336517","doi":"https://doi.org/10.1142/s0218127407018221","title":"DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART I: KNOTS, LINKS AND CHAOS","display_name":"DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART I: KNOTS, LINKS AND CHAOS","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2034336517","doi":"https://doi.org/10.1142/s0218127407018221","mag":"2034336517"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407018221","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407018221","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0706.2416","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"YI SONG","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"YI SONG","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":null,"display_name":"STEPHEN P. BANKS","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"STEPHEN P. BANKS","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"last","author":{"id":null,"display_name":"DAVID DIAZ","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"DAVID DIAZ","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I91136226"],"apc_list":null,"apc_paid":null,"fwci":0.4544,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61436453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"06","first_page":"2073","last_page":"2084"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.8593999743461609,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.8593999743461609,"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":0.036400001496076584,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.007199999876320362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.704200029373169},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.6783999800682068},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.550599992275238},{"id":"https://openalex.org/keywords/braid","display_name":"Braid","score":0.532800018787384},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5131000280380249},{"id":"https://openalex.org/keywords/knot","display_name":"Knot (papermaking)","score":0.48069998621940613},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.4609000086784363},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.4458000063896179},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.375900000333786}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.704200029373169},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6783999800682068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5824000239372253},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.550599992275238},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.532800018787384},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5131000280380249},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.48069998621940613},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.4609000086784363},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.4458000063896179},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38589999079704285},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C143330242","wikidata":"https://www.wikidata.org/wiki/Q849798","display_name":"Knot theory","level":3,"score":0.37299999594688416},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.3619000017642975},{"id":"https://openalex.org/C175197506","wikidata":"https://www.wikidata.org/wiki/Q1003225","display_name":"Measure-preserving dynamical system","level":5,"score":0.3531000018119812},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28459998965263367},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.2639999985694885},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127407018221","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407018221","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:arXiv.org:0706.2416","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0706.2416","pdf_url":"https://arxiv.org/pdf/0706.2416","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0706.2416","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0706.2416","pdf_url":"https://arxiv.org/pdf/0706.2416","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W390606","https://openalex.org/W1551417921","https://openalex.org/W1967797812","https://openalex.org/W2042043617","https://openalex.org/W2163049309","https://openalex.org/W4255075412"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,73],"give":[4],"an":[5],"explicit":[6,64],"construction":[7],"of":[8,35,84],"dynamical":[9,68],"systems":[10,69],"(defined":[11],"within":[12],"a":[13,38,48,53,76,81],"solid":[14],"torus)":[15],"containing":[16,40,70],"any":[17],"knot":[18],"(or":[19],"link)":[20],"and":[21,43,55],"arbitrarily":[22],"knotted":[23,60],"chaos.":[24],"The":[25,87],"first":[26],"is":[27,93],"achieved":[28],"by":[29,95],"expressing":[30],"the":[31,41,58,71,85,97],"knots":[32],"in":[33],"terms":[34],"braids,":[36,72],"defining":[37],"system":[39,49],"braids":[42],"extending":[44],"periodically":[45],"to":[46,79],"obtain":[47],"naturally":[50],"defined":[51],"on":[52],"torus":[54],"which":[56],"contains":[57],"given":[59],"trajectories.":[61],"To":[62],"get":[63],"differential":[65],"equations":[66],"for":[67],"will":[74],"use":[75],"certain":[77],"function":[78],"define":[80],"tube":[82],"neighborhood":[83],"braid.":[86],"second":[88],"one,":[89],"generating":[90],"chaotic":[91],"systems,":[92],"realized":[94],"modeling":[96],"Smale":[98],"horseshoe.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2016-06-24T00:00:00"}