{"id":"https://openalex.org/W2040093998","doi":"https://doi.org/10.1142/s0218127402006308","title":"THE NATURAL MEASURE OF NONATTRACTING CHAOTIC SETS AND ITS REPRESENTATION BY UNSTABLE PERIODIC ORBITS","display_name":"THE NATURAL MEASURE OF NONATTRACTING CHAOTIC SETS AND ITS REPRESENTATION BY UNSTABLE PERIODIC ORBITS","publication_year":2002,"publication_date":"2002-12-01","ids":{"openalex":"https://openalex.org/W2040093998","doi":"https://doi.org/10.1142/s0218127402006308","mag":"2040093998"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127402006308","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127402006308","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":["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/A5110341532","display_name":"Mukeshwar Dhamala","orcid":null},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]},{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"MUKESHWAR DHAMALA","raw_affiliation_strings":["School of Medicine, Emory University, Atlanta,  GA 30322, USA","School of Physics, Georgia Institute of Technology,  Atlanta, GA 30332, USA","School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA","School of Medicine, Emory University, Atlanta, GA 30322, USA"],"affiliations":[{"raw_affiliation_string":"School of Medicine, Emory University, Atlanta,  GA 30322, USA","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"School of Physics, Georgia Institute of Technology,  Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of Medicine, Emory University, Atlanta, GA 30322, USA","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102995786","display_name":"Ying\u2010Cheng Lai","orcid":"https://orcid.org/0000-0002-0723-733X"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"YING-CHENG LAI","raw_affiliation_strings":["Departments of Mathematics and Electrical Engineering, Systems Science and Engineering Research Center, Arizona State University,  Tempe, AZ 85287, USA","Departments of Mathematics and Electrical Engineering, Systems Science and Engineering Research Center, Arizona State University, Tempe, AZ 85287, USA"],"affiliations":[{"raw_affiliation_string":"Departments of Mathematics and Electrical Engineering, Systems Science and Engineering Research Center, Arizona State University,  Tempe, AZ 85287, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Departments of Mathematics and Electrical Engineering, Systems Science and Engineering Research Center, Arizona State University, Tempe, AZ 85287, USA","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110341532"],"corresponding_institution_ids":["https://openalex.org/I130701444","https://openalex.org/I150468666"],"apc_list":null,"apc_paid":null,"fwci":1.851,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8307771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"12","first_page":"2991","last_page":"3005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9977999925613403,"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/T10244","display_name":"Chaos control and synchronization","score":0.9972000122070312,"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/chaotic","display_name":"Chaotic","score":0.7398317456245422},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6662957668304443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.636812686920166},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.6041074395179749},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5340408682823181},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.5033382773399353},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.49901700019836426},{"id":"https://openalex.org/keywords/crisis","display_name":"Crisis","score":0.48500391840934753},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4721280038356781},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.4492345452308655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4420018196105957},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.42957544326782227},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3942979872226715},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.3267369866371155},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22703874111175537},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.19521671533584595},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.16423338651657104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14703747630119324},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.08815711736679077},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.07441985607147217},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06301850080490112}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7398317456245422},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6662957668304443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.636812686920166},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.6041074395179749},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5340408682823181},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5033382773399353},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.49901700019836426},{"id":"https://openalex.org/C78302928","wikidata":"https://www.wikidata.org/wiki/Q5185947","display_name":"Crisis","level":4,"score":0.48500391840934753},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4721280038356781},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.4492345452308655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4420018196105957},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.42957544326782227},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3942979872226715},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.3267369866371155},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22703874111175537},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.19521671533584595},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.16423338651657104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14703747630119324},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08815711736679077},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07441985607147217},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06301850080490112},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace 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},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127402006308","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127402006308","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:CiteSeerX.psu:10.1.1.418.5585","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.418.5585","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://chaos1.la.asu.edu/~yclai/papers/IJBC_02_DL.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1966285388","https://openalex.org/W1967429562","https://openalex.org/W1967907848","https://openalex.org/W1969221972","https://openalex.org/W1976022108","https://openalex.org/W1980039556","https://openalex.org/W1982188993","https://openalex.org/W1986425174","https://openalex.org/W1989421522","https://openalex.org/W1991346547","https://openalex.org/W1992120986","https://openalex.org/W1996767607","https://openalex.org/W2001483689","https://openalex.org/W2007842217","https://openalex.org/W2008486579","https://openalex.org/W2015451024","https://openalex.org/W2016173714","https://openalex.org/W2016182590","https://openalex.org/W2022382501","https://openalex.org/W2032259428","https://openalex.org/W2035286224","https://openalex.org/W2037254051","https://openalex.org/W2043060607","https://openalex.org/W2045184052","https://openalex.org/W2051430830","https://openalex.org/W2060708093","https://openalex.org/W2061980825","https://openalex.org/W2062427814","https://openalex.org/W2070111669","https://openalex.org/W2074624925","https://openalex.org/W2082822557","https://openalex.org/W2084164774","https://openalex.org/W2084810398","https://openalex.org/W2086126610","https://openalex.org/W2087045023","https://openalex.org/W2087159195","https://openalex.org/W2089968197","https://openalex.org/W2090532902","https://openalex.org/W2092152122","https://openalex.org/W2094228886","https://openalex.org/W2095163191","https://openalex.org/W2125566231","https://openalex.org/W2126933998","https://openalex.org/W2165510765","https://openalex.org/W4212928962","https://openalex.org/W4229497514","https://openalex.org/W4255965261"],"related_works":["https://openalex.org/W2392447668","https://openalex.org/W1496745782","https://openalex.org/W1581278046","https://openalex.org/W2152993703","https://openalex.org/W2387089906","https://openalex.org/W1996419866","https://openalex.org/W2810202354","https://openalex.org/W4240432832","https://openalex.org/W129814329","https://openalex.org/W1998049234"],"abstract_inverted_index":{"The":[0,45],"natural":[1,79,157],"measure":[2,80,158],"of":[3,18,47,77,111,155],"a":[4,8,83,118],"chaotic":[5,26,42,60,88,163],"set":[6,27],"in":[7,24,29,67,98],"phase-space":[9],"region":[10],"can":[11,142],"be":[12,38,143],"related":[13],"to":[14,37,51,57,64,90,117,147,161],"the":[15,25,75,78,87,99,104,107,131,135,148,151,156],"dynamical":[16],"properties":[17],"all":[19],"unstable":[20,94,125,152],"periodic":[21,95,126,140],"orbits":[22,96,141],"embedded":[23,97],"contained":[28],"that":[30,91,150],"region.":[31],"This":[32],"result":[33,55],"has":[34],"been":[35],"shown":[36],"valid":[39],"for":[40,138],"hyperbolic":[41],"invariant":[43],"sets.":[44],"aim":[46],"this":[48,54],"paper":[49],"is":[50,159],"examine":[52],"whether":[53],"applies":[56],"nonhyperbolic,":[58],"nonattracting":[59],"saddles":[61],"which":[62,139],"lead":[63],"transient":[65],"chaos":[66],"physical":[68,112],"systems.":[69],"In":[70],"particular,":[71],"we":[72],"examine,":[73],"quantitatively,":[74],"closeness":[76],"obtained":[81],"from":[82,93,124],"long":[84],"trajectory":[85,120],"on":[86],"saddle":[89],"evaluated":[92,114],"set.":[100],"We":[101],"also":[102],"analyze":[103],"difference":[105],"between":[106],"long-time":[108],"average":[109],"values":[110],"quantities":[113],"with":[115,129],"respect":[116],"dense":[119],"and":[121,134],"those":[122],"computed":[123],"orbits.":[127],"Results":[128],"both":[130],"H\u00e9non":[132],"map":[133,137],"Ikeda\u2013Hammel\u2013Jones\u2013Moloney":[136],"enumerated":[144],"lend":[145],"credence":[146],"conjecture":[149],"periodic-orbit":[153],"theory":[154],"applicable":[160],"nonhyperbolic":[162],"saddles.":[164]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
