{"id":"https://openalex.org/W2781801733","doi":"https://doi.org/10.1142/s0218127417502054","title":"Exact Torus Knot Periodic Orbits and Homoclinic Orbits in a Class of Three-Dimensional Flows Generated by a Planar Cubic System","display_name":"Exact Torus Knot Periodic Orbits and Homoclinic Orbits in a Class of Three-Dimensional Flows Generated by a Planar Cubic System","publication_year":2017,"publication_date":"2017-12-15","ids":{"openalex":"https://openalex.org/W2781801733","doi":"https://doi.org/10.1142/s0218127417502054","mag":"2781801733"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417502054","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5086628608","display_name":"Tonghua Zhang","orcid":"https://orcid.org/0000-0003-0510-1428"},"institutions":[{"id":"https://openalex.org/I57093077","display_name":"Swinburne University of Technology","ror":"https://ror.org/031rekg67","country_code":"AU","type":"education","lineage":["https://openalex.org/I57093077"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Tonghua Zhang","raw_affiliation_strings":["Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia","institution_ids":["https://openalex.org/I57093077"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100599691","display_name":"Jibin Li","orcid":"https://orcid.org/0000-0003-4839-5956"},"institutions":[{"id":"https://openalex.org/I119045251","display_name":"Huaqiao University","ror":"https://ror.org/03frdh605","country_code":"CN","type":"education","lineage":["https://openalex.org/I119045251"]},{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jibin Li","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China","institution_ids":["https://openalex.org/I119045251"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100599691"],"corresponding_institution_ids":["https://openalex.org/I119045251","https://openalex.org/I135237710"],"apc_list":null,"apc_paid":null,"fwci":0.418,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":3,"citation_normalized_percentile":{"value":0.439154,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":75,"max":77},"biblio":{"volume":"27","issue":"13","first_page":"1750205","last_page":"1750205"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9947,"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":0.9947,"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":0.983,"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":0.974,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.574647}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9185933},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.8389071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.61052424},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.59568435},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.574647},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.5118824},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5087159},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4992044},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4599068},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42793036},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31155205},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22326806},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.14503223},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.08472067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0769431},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07084304},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417502054","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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China","award_id":"11571318"},{"funder":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China","award_id":"11471289"}],"datasets":[],"versions":[],"referenced_works_count":23,"referenced_works":["https://openalex.org/W1901023941","https://openalex.org/W1967307154","https://openalex.org/W1967797812","https://openalex.org/W1969016693","https://openalex.org/W1975421333","https://openalex.org/W1985460229","https://openalex.org/W1999304929","https://openalex.org/W2006642504","https://openalex.org/W2008128550","https://openalex.org/W2013724384","https://openalex.org/W2017348434","https://openalex.org/W2051739407","https://openalex.org/W2054147240","https://openalex.org/W2061606808","https://openalex.org/W2079411970","https://openalex.org/W2134820765","https://openalex.org/W3098450610","https://openalex.org/W390606","https://openalex.org/W4236057051","https://openalex.org/W4253904265","https://openalex.org/W4255289997","https://openalex.org/W64821788","https://openalex.org/W9726823"],"related_works":["https://openalex.org/W4286418818","https://openalex.org/W4229571370","https://openalex.org/W3004031260","https://openalex.org/W2952057549","https://openalex.org/W2167841308","https://openalex.org/W2162480247","https://openalex.org/W2147240237","https://openalex.org/W2116505584","https://openalex.org/W1994449808","https://openalex.org/W1984913125"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"a":[3,10],"class":[4,50],"of":[5,35,51,58,67,72],"three-dimensional":[6],"systems":[7,52],"constructed":[8],"by":[9],"rotating":[11],"planar":[12],"symmetric":[13],"cubic":[14],"vector":[15],"field.":[16],"To":[17],"study":[18,46],"its":[19],"periodic":[20,36,60,77],"orbits":[21,37,78],"including":[22],"homoclinic":[23],"orbits,":[24,61],"which":[25,62],"may":[26],"be":[27],"knotted":[28,59],"in":[29],"space,":[30],"we":[31],"classify":[32],"the":[33],"types":[34,57],"and":[38],"then":[39],"calculate":[40],"their":[41],"exact":[42],"parametric":[43],"representations.":[44],"Our":[45],"shows":[47],"that":[48],"this":[49],"has":[53],"infinitely":[54],"many":[55],"distinct":[56],"lie":[63],"on":[64],"three":[65],"families":[66],"invariant":[68],"tori.":[69],"Numerical":[70],"examples":[71],"[Formula:":[73],"see":[74],"text]-torus":[75],"knot":[76],"have":[79],"also":[80],"been":[81],"provided":[82],"to":[83],"illustrate":[84],"our":[85],"theoretical":[86],"results.":[87]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2781801733","counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2024-12-07T13:59:28.038898","created_date":"2018-01-12"}