{"id":"https://openalex.org/W1556084640","doi":"https://doi.org/10.1142/s0218127416501315","title":"Chaotic Polynomial Maps","display_name":"Chaotic Polynomial Maps","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W1556084640","doi":"https://doi.org/10.1142/s0218127416501315","mag":"1556084640"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416501315","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501315","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/1502.05446","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100437233","display_name":"Xu Zhang","orcid":"https://orcid.org/0000-0002-5138-6631"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xu Zhang","raw_affiliation_strings":["Department of Mathematics, Shandong University, Weihai, Shandong 264209, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Weihai, Shandong 264209, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100437233"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":null,"apc_paid":null,"fwci":1.8015,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.80681818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"08","first_page":"1650131","last_page":"1650131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9998999834060669,"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":0.9998999834060669,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9987999796867371,"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/T10244","display_name":"Chaos control and synchronization","score":0.9962000250816345,"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/mathematics","display_name":"Mathematics","score":0.7487620711326599},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.64603590965271},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6368007659912109},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.5845050811767578},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5614414215087891},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5517536997795105},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.5285781025886536},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.4896593689918518},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.484826922416687},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.45517897605895996},{"id":"https://openalex.org/keywords/subshift-of-finite-type","display_name":"Subshift of finite type","score":0.44837486743927},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44730186462402344},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3328915238380432},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2934507727622986},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15482482314109802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08607202768325806}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7487620711326599},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.64603590965271},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6368007659912109},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.5845050811767578},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5614414215087891},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5517536997795105},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.5285781025886536},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.4896593689918518},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.484826922416687},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.45517897605895996},{"id":"https://openalex.org/C105932330","wikidata":"https://www.wikidata.org/wiki/Q7631990","display_name":"Subshift of finite type","level":2,"score":0.44837486743927},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44730186462402344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3328915238380432},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2934507727622986},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15482482314109802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08607202768325806},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127416501315","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501315","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:1502.05446","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.05446","pdf_url":"https://arxiv.org/pdf/1502.05446","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:1502.05446","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.05446","pdf_url":"https://arxiv.org/pdf/1502.05446","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1556084640.pdf","grobid_xml":"https://content.openalex.org/works/W1556084640.grobid-xml"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W900012","https://openalex.org/W196973002","https://openalex.org/W606609856","https://openalex.org/W1558526027","https://openalex.org/W1589876408","https://openalex.org/W1832629464","https://openalex.org/W1937868048","https://openalex.org/W1967599194","https://openalex.org/W1973729576","https://openalex.org/W1973889959","https://openalex.org/W1981267194","https://openalex.org/W1984029601","https://openalex.org/W1989097268","https://openalex.org/W1991100653","https://openalex.org/W1991326063","https://openalex.org/W1998538686","https://openalex.org/W1998727969","https://openalex.org/W2005070052","https://openalex.org/W2008995486","https://openalex.org/W2010487867","https://openalex.org/W2017647225","https://openalex.org/W2022970946","https://openalex.org/W2025802652","https://openalex.org/W2027415339","https://openalex.org/W2030813267","https://openalex.org/W2035678129","https://openalex.org/W2050486738","https://openalex.org/W2050559829","https://openalex.org/W2057959049","https://openalex.org/W2059340344","https://openalex.org/W2059545648","https://openalex.org/W2062082027","https://openalex.org/W2064468215","https://openalex.org/W2077684023","https://openalex.org/W2078590371","https://openalex.org/W2079828446","https://openalex.org/W2081461845","https://openalex.org/W2093700670","https://openalex.org/W2095288649","https://openalex.org/W2102892532","https://openalex.org/W2108466946","https://openalex.org/W2109633131","https://openalex.org/W2123092877","https://openalex.org/W2125566231","https://openalex.org/W2127216059","https://openalex.org/W2127693037","https://openalex.org/W2141394518","https://openalex.org/W2145779207","https://openalex.org/W2158361993","https://openalex.org/W2162144003","https://openalex.org/W2163678030","https://openalex.org/W2170048119","https://openalex.org/W2186405113","https://openalex.org/W2315759974","https://openalex.org/W2577900305","https://openalex.org/W2951206354","https://openalex.org/W2989058889","https://openalex.org/W3098146138","https://openalex.org/W3137137946","https://openalex.org/W4231102510","https://openalex.org/W4239398473","https://openalex.org/W4241263920","https://openalex.org/W4247961814","https://openalex.org/W4256081943","https://openalex.org/W4294967943","https://openalex.org/W4302776623"],"related_works":["https://openalex.org/W2770002227","https://openalex.org/W2041581981","https://openalex.org/W2368534455","https://openalex.org/W2919808355","https://openalex.org/W2107919623","https://openalex.org/W2471026571","https://openalex.org/W2124001337","https://openalex.org/W3003204361","https://openalex.org/W4245801504","https://openalex.org/W2134842291"],"abstract_inverted_index":{"This":[0,47],"paper":[1],"introduces":[2],"a":[3],"class":[4],"of":[5,43,49,126],"polynomial":[6,128],"maps":[7,37,50,129,154,170],"in":[8,40,72,178],"Euclidean":[9],"spaces,":[10,74],"investigates":[11],"the":[12,26,41,53,57,64,75,90,96,108,115,119,133,149,153,156,160,188,196],"conditions":[13,76,134],"under":[14,77,135],"which":[15,78,89,136],"there":[16,79,137],"exist":[17,80],"Smale":[18,81,139],"horseshoes":[19,82,140],"and":[20,30,33,56,83,118,141,148,159,174],"uniformly":[21,84,142],"hyperbolic":[22,85,143],"invariant":[23,86,144,157],"sets,":[24],"studies":[25],"chaotic":[27,39,109,172],"dynamical":[28],"behavior":[29],"strange":[31],"attractors,":[32],"shows":[34],"that":[35],"some":[36,61,105],"are":[38,92,102,138,146,181,192],"sense":[42],"Li\u2013Yorke":[44],"or":[45,70],"Devaney.":[46],"type":[48],"includes":[51],"both":[52],"Logistic":[54],"map":[55],"H\u00e9non":[58],"map.":[59],"For":[60,123],"diffeomorphisms":[62],"with":[63,130,171],"expansion":[65],"dimension":[66],"equal":[67],"to":[68,95,194],"one":[69],"two":[71,190],"three-dimensional":[73,179],"sets":[87,145,158],"on":[88,99,155,163],"systems":[91],"topologically":[93],"conjugate":[94],"two-sided":[97,161],"fullshift":[98,162],"finite":[100,164],"alphabet":[101,165],"obtained;":[103],"for":[104],"expanding":[106],"maps,":[107],"region":[110],"is":[111,166],"analyzed":[112],"by":[113,183],"using":[114,184],"coupled-expansion":[116],"theory":[117],"Brouwer":[120],"degree":[121,131],"theory.":[122],"three":[124],"types":[125],"higher-dimensional":[127],"two,":[132],"given,":[147],"topological":[150],"conjugacy":[151],"between":[152],"obtained.":[167],"Some":[168],"interesting":[169],"attractors":[173],"positive":[175],"Lyapunov":[176],"exponents":[177],"spaces":[180],"found":[182],"computer":[185],"simulations.":[186],"In":[187],"end,":[189],"examples":[191],"provided":[193],"illustrate":[195],"theoretical":[197],"results.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2025-10-10T00:00:00"}
