{"id":"https://openalex.org/W2461143329","doi":"https://doi.org/10.1142/s021812741650084x","title":"Invariant Spectra in N-Coupled Standard Maps","display_name":"Invariant Spectra in N-Coupled Standard Maps","publication_year":2016,"publication_date":"2016-05-01","ids":{"openalex":"https://openalex.org/W2461143329","doi":"https://doi.org/10.1142/s021812741650084x","mag":"2461143329"},"language":"en","primary_location":{"id":"doi:10.1142/s021812741650084x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741650084x","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/A5080379161","display_name":"G. Livadiotis","orcid":"https://orcid.org/0000-0002-7655-6019"},"institutions":[{"id":"https://openalex.org/I1290463931","display_name":"Southwest Research Institute","ror":"https://ror.org/03tghng59","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1290463931"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George Livadiotis","raw_affiliation_strings":["Southwest Research Institute, San Antonio, TX 78238, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Southwest Research Institute, San Antonio, TX 78238, USA","institution_ids":["https://openalex.org/I1290463931"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080379161"],"corresponding_institution_ids":["https://openalex.org/I1290463931"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05798117,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"26","issue":"05","first_page":"1650084","last_page":"1650084"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9948999881744385,"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":0.9916999936103821,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.7054288387298584},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6610991954803467},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.6603698134422302},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.6507469415664673},{"id":"https://openalex.org/keywords/spectral-line","display_name":"Spectral line","score":0.6187345385551453},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5873066782951355},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5634715557098389},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5337356925010681},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5329870581626892},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.479541540145874},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4631013572216034},{"id":"https://openalex.org/keywords/standard-map","display_name":"Standard map","score":0.44957244396209717},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4323734939098358},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.40559980273246765},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3879801630973816},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37388676404953003},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.28649938106536865},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.2396748960018158},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1713533103466034},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12770295143127441},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10682043433189392}],"concepts":[{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.7054288387298584},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6610991954803467},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.6603698134422302},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6507469415664673},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.6187345385551453},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5873066782951355},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5634715557098389},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5337356925010681},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5329870581626892},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.479541540145874},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4631013572216034},{"id":"https://openalex.org/C82229145","wikidata":"https://www.wikidata.org/wiki/Q2257676","display_name":"Standard map","level":3,"score":0.44957244396209717},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4323734939098358},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40559980273246765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3879801630973816},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37388676404953003},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.28649938106536865},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2396748960018158},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1713533103466034},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12770295143127441},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10682043433189392},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical 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":[{"id":"doi:10.1142/s021812741650084x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741650084x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1981035988","https://openalex.org/W2001082993","https://openalex.org/W2063553794","https://openalex.org/W2082410277","https://openalex.org/W2091111385","https://openalex.org/W2103388492","https://openalex.org/W2144621465","https://openalex.org/W2277420092","https://openalex.org/W3098607799"],"related_works":["https://openalex.org/W142914808","https://openalex.org/W4225342163","https://openalex.org/W4293402875","https://openalex.org/W1560843892","https://openalex.org/W2054229853","https://openalex.org/W3013851045","https://openalex.org/W2794025271","https://openalex.org/W4300561179","https://openalex.org/W2964291893","https://openalex.org/W1530927473"],"abstract_inverted_index":{"This":[0,47,61],"paper":[1],"examines":[2],"the":[3,6,25,29,38,44,57,67,70,76,88],"evolution":[4],"of":[5,9,15,28,37,59,69],"dynamical":[7,83],"spectra":[8,30,84],"stretching":[10,78],"numbers":[11],"in":[12],"a":[13],"system":[14],"[Formula:":[16],"see":[17,41],"text]-coupled":[18],"Standard":[19],"Maps.":[20],"It":[21,80],"is":[22,35,49,63],"found":[23],"that":[24,82],"convergence":[26],"rate":[27,48],"to":[31],"their":[32],"invariant":[33],"forms":[34],"independent":[36],"dimensionality":[39],"2[Formula:":[40],"text]":[42],"and":[43],"nonlinearity/coupling":[45],"parameters.":[46],"impressively":[50],"faster":[51],"than":[52],"one":[53],"could":[54],"predict":[55],"on":[56,87],"basis":[58],"ergodicity.":[60],"effect":[62],"probably":[64],"associated":[65],"with":[66],"manifold":[68],"maximum":[71],"Lyapunov":[72],"exponent":[73],"along":[74],"which":[75],"main":[77],"occurs.":[79],"seems":[81],"depend":[85],"mainly":[86],"dramatically":[89],"smaller":[90],"subspace":[91],"defined":[92],"by":[93],"this":[94],"unstable":[95],"manifold.":[96]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
