{"id":"https://openalex.org/W1999667128","doi":"https://doi.org/10.1155/2013/287123","title":"The Related Extension and Application of the \u0160i'lnikov Theorem","display_name":"The Related Extension and Application of the \u0160i'lnikov Theorem","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1999667128","doi":"https://doi.org/10.1155/2013/287123","mag":"1999667128"},"language":"en","primary_location":{"id":"doi:10.1155/2013/287123","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/287123","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/287123.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/287123.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066140816","display_name":"Baoying Chen","orcid":"https://orcid.org/0000-0002-9998-6433"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Baoying Chen","raw_affiliation_strings":["Department of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China","institution_ids":["https://openalex.org/I139024713"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066140816"],"corresponding_institution_ids":["https://openalex.org/I139024713"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.2287,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.53884248,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9991000294685364,"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/T10244","display_name":"Chaos control and synchronization","score":0.9991000294685364,"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":0.9966999888420105,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9919000267982483,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9237817525863647},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.8339142799377441},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6774648427963257},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6237310171127319},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5063284635543823},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.46871107816696167},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4392067790031433},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3863326609134674},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1987968385219574},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.07757580280303955},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05309060215950012}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9237817525863647},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.8339142799377441},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6774648427963257},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6237310171127319},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5063284635543823},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.46871107816696167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4392067790031433},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3863326609134674},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1987968385219574},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.07757580280303955},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05309060215950012},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/287123","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/287123","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/287123.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394807888","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394807888","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:287123","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/287123.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:ff2c16d81a5f4713b6b05242881f7ba7","is_oa":true,"landing_page_url":"https://doaj.org/article/ff2c16d81a5f4713b6b05242881f7ba7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/287123","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/287123","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/287123.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1999667128.pdf","grobid_xml":"https://content.openalex.org/works/W1999667128.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1974327486","https://openalex.org/W1994859578","https://openalex.org/W2014748151","https://openalex.org/W2024306217","https://openalex.org/W2066340280","https://openalex.org/W2078298500","https://openalex.org/W2083531786","https://openalex.org/W2092360752","https://openalex.org/W2092680287","https://openalex.org/W2114810947","https://openalex.org/W2126098770","https://openalex.org/W2130618526","https://openalex.org/W2152532612","https://openalex.org/W2314906218","https://openalex.org/W2408718584"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2363992932","https://openalex.org/W2910725637","https://openalex.org/W2043723919","https://openalex.org/W2066340280","https://openalex.org/W1999123830","https://openalex.org/W1593713154","https://openalex.org/W2971991931","https://openalex.org/W2054807178","https://openalex.org/W2759184667"],"abstract_inverted_index":{"The":[0],"traditional":[1],"\u0160i'lnikov":[2,25,56,72,92,113],"theorems":[3],"provide":[4],"analytic":[5],"criteria":[6],"for":[7],"proving":[8],"the":[9,24,38,43,51,55,71,87,109,112],"existence":[10],"of":[11,23,33,45,54,70,111],"chaos":[12,41],"in":[13,42,89,108],"high-dimensional":[14],"autonomous":[15,101],"systems.":[16],"We":[17,65],"have":[18,29],"established":[19],"one":[20],"extended":[21,68,91],"version":[22,69],"homoclinic":[26,57,73,93],"theorem":[27,58],"and":[28,59,105],"given":[30],"a":[31,79],"set":[32],"sufficient":[34],"conditions":[35,88],"under":[36],"which":[37,84],"system":[39,83],"generates":[40],"sense":[44],"Smale":[46],"horseshoes.":[47],"In":[48,75],"this":[49,90],"paper,":[50],"extension":[52],"questions":[53],"its":[60],"applications":[61],"are":[62],"still":[63],"discussed.":[64],"establish":[66],"another":[67],"theorem.":[74,94],"addition,":[76],"we":[77,96],"construct":[78],"new":[80],"three-dimensional":[81,100],"chaotic":[82,103],"meets":[85],"all":[86,98],"Finally,":[95],"list":[97],"well-known":[99],"quadratic":[102],"systems":[104],"classify":[106],"them":[107],"light":[110],"theorems.":[114]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}