{"id":"https://openalex.org/W2089838496","doi":"https://doi.org/10.1142/s0218127412502173","title":"ESTIMATING HYPERBOLICITY OF CHAOTIC BIDIMENSIONAL MAPS","display_name":"ESTIMATING HYPERBOLICITY OF CHAOTIC BIDIMENSIONAL MAPS","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W2089838496","doi":"https://doi.org/10.1142/s0218127412502173","mag":"2089838496"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127412502173","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412502173","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/1206.3986","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103808309","display_name":"Matteo Sala","orcid":null},"institutions":[{"id":"https://openalex.org/I115752224","display_name":"University of Insubria","ror":"https://ror.org/00s409261","country_code":"IT","type":"education","lineage":["https://openalex.org/I115752224"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"MATTEO SALA","raw_affiliation_strings":["Center for Nonlinear and Complex Systems, Universit\u00e0 dell'Insubria, Via Valleggio 11, Como 22100, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Nonlinear and Complex Systems, Universit\u00e0 dell'Insubria, Via Valleggio 11, Como 22100, Italy","institution_ids":["https://openalex.org/I115752224"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018328761","display_name":"Cesar Manchein","orcid":"https://orcid.org/0000-0001-8786-3893"},"institutions":[{"id":"https://openalex.org/I164790352","display_name":"Universidade do Estado de Santa Catarina","ror":"https://ror.org/03ztsbk67","country_code":"BR","type":"education","lineage":["https://openalex.org/I164790352"]},{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"CESAR MANCHEIN","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Federal do Paran\u00e0, 81531-980 Curitiba, PR, Brazil","Departamento de F\u00edsica, Universidade do Estado de Santa Catarina, 89219-710 Joinville, SC, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Federal do Paran\u00e0, 81531-980 Curitiba, PR, Brazil","institution_ids":["https://openalex.org/I52418104"]},{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina, 89219-710 Joinville, SC, Brazil","institution_ids":["https://openalex.org/I164790352"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046338711","display_name":"Roberto Artuso","orcid":"https://orcid.org/0000-0002-6463-1093"},"institutions":[{"id":"https://openalex.org/I115752224","display_name":"University of Insubria","ror":"https://ror.org/00s409261","country_code":"IT","type":"education","lineage":["https://openalex.org/I115752224"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"ROBERTO ARTUSO","raw_affiliation_strings":["Center for Nonlinear and Complex Systems, Universit\u00e0 dell'Insubria, Via Valleggio 11, Como 22100, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Nonlinear and Complex Systems, Universit\u00e0 dell'Insubria, Via Valleggio 11, Como 22100, Italy","institution_ids":["https://openalex.org/I115752224"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103808309"],"corresponding_institution_ids":["https://openalex.org/I115752224"],"apc_list":null,"apc_paid":null,"fwci":0.2427,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.57492675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"09","first_page":"1250217","last_page":"1250217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9975000023841858,"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":0.9975000023841858,"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":0.9969000220298767,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9786999821662903,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7546529769897461},{"id":"https://openalex.org/keywords/transversality","display_name":"Transversality","score":0.7084416747093201},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6900475025177002},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6829279661178589},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.5838450789451599},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5374295115470886},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.47998854517936707},{"id":"https://openalex.org/keywords/covariant-transformation","display_name":"Covariant transformation","score":0.45063111186027527},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44039005041122437},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35180675983428955},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16976100206375122},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14002391695976257},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09740036725997925},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07416722178459167}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7546529769897461},{"id":"https://openalex.org/C24167531","wikidata":"https://www.wikidata.org/wiki/Q2300767","display_name":"Transversality","level":2,"score":0.7084416747093201},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6900475025177002},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6829279661178589},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5838450789451599},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5374295115470886},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.47998854517936707},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.45063111186027527},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44039005041122437},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35180675983428955},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16976100206375122},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14002391695976257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09740036725997925},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07416722178459167},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0218127412502173","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412502173","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:1206.3986","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1206.3986","pdf_url":"https://arxiv.org/pdf/1206.3986","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"},{"id":"pmh:oai:repositorio.udesc.br:UDESC/9343","is_oa":true,"landing_page_url":"https://repositorio.udesc.br/handle/UDESC/9343","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UDESC","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:urlib.net:sid.inpe.br/mtc-m19/2010/09.20.13.19.01-0","is_oa":false,"landing_page_url":"http://urlib.net/sid.inpe.br/mtc-m19/2010/09.20.13.19","pdf_url":null,"source":{"id":"https://openalex.org/S4377196298","display_name":"Biblioteca Digital da Mem\u00f3ria Cient\u00edfica do INPE (National Institute for Space Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I80849659","host_organization_name":"Instituto Nacional de Pesquisas Espaciais","host_organization_lineage":["https://openalex.org/I80849659"],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1206.3986","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1206.3986","pdf_url":"https://arxiv.org/pdf/1206.3986","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":[{"score":0.5400000214576721,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1985807095","https://openalex.org/W1987426536","https://openalex.org/W2000983461","https://openalex.org/W2025337303","https://openalex.org/W2025551626","https://openalex.org/W2040161185","https://openalex.org/W2071890556","https://openalex.org/W2073074358","https://openalex.org/W2078409350","https://openalex.org/W2111260035","https://openalex.org/W2125566231","https://openalex.org/W2167469018","https://openalex.org/W4205233157","https://openalex.org/W4230237964","https://openalex.org/W4294967943","https://openalex.org/W4388391905"],"related_works":["https://openalex.org/W2045665826","https://openalex.org/W155037358","https://openalex.org/W4240610494","https://openalex.org/W2980627813","https://openalex.org/W3006004107","https://openalex.org/W2615244697","https://openalex.org/W2895586195","https://openalex.org/W1748295019","https://openalex.org/W125373334","https://openalex.org/W2081531990"],"abstract_inverted_index":{"We":[0],"apply":[1],"to":[2,15,37,61,84,94,155],"bidimensional":[3],"chaotic":[4],"maps":[5],"the":[6,17,22,29,38,44,54,63,86,106,112,138,156],"numerical":[7],"method":[8],"proposed":[9],"by":[10,28,125],"Ginelli":[11],"et":[12],"al.":[13],"[2007]":[14],"approximate":[16],"associated":[18],"Oseledets":[19],"splitting,":[20],"i.e.":[21],"set":[23],"of":[24,46,65,67,78,88,115,141],"linear":[25,127],"subspaces":[26,42],"spanned":[27],"so-called":[30],"covariant":[31],"Lyapunov":[32,39],"vectors":[33],"(CLV)":[34],"and":[35,160],"corresponding":[36],"spectrum.":[40],"These":[41],"are":[43,123,147],"analog":[45],"linearized":[47],"invariant":[48],"manifolds":[49],"for":[50,117],"nonperiodic":[51],"points,":[52],"so":[53],"angles":[55,132,143],"between":[56],"them":[57],"can":[58],"be":[59,171],"used":[60],"quantify":[62],"degree":[64],"hyperbolicity":[66],"generic":[68],"orbits;":[69],"however,":[70],"such":[71,168],"splitting":[72,131],"being":[73],"noninvariant":[74],"under":[75],"smooth":[76],"transformations":[77],"phase":[79,134],"space,":[80,135],"it":[81,96],"is":[82,152],"interesting":[83],"investigate":[85],"properties":[87],"transversality":[89,116],"when":[90],"coordinates":[91],"change,":[92],"e.g.":[93],"study":[95],"in":[97,148],"distinct":[98],"dynamical":[99],"systems.":[100],"To":[101],"illustrate":[102],"this":[103],"issue":[104],"on":[105],"Chirikov\u2013Taylor":[107],"standard":[108],"map,":[109],"we":[110],"compare":[111],"probability":[113,139],"densities":[114],"two":[118],"different":[119],"coordinate":[120],"systems;":[121],"these":[122],"connected":[124],"a":[126],"transformation":[128,158],"that":[129,163],"deforms":[130],"through":[133],"changing":[136],"also":[137],"density":[140],"almost-zero":[142],"although":[144],"complete":[145],"tangencies":[146],"fact":[149],"invariant.":[150],"This":[151],"completely":[153],"due":[154],"PDF":[157],"law":[159],"strongly":[161],"suggests":[162],"any":[164],"statistical":[165],"inference":[166],"from":[167],"distributions":[169],"must":[170],"generally":[172],"taken":[173],"with":[174],"care.":[175]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-11-23T00:00:00"}
