{"id":"https://openalex.org/W2160884680","doi":"https://doi.org/10.1142/s021812741250215x","title":"ANALYSIS OF ROUND OFF ERRORS WITH REVERSIBILITY TEST AS A DYNAMICAL INDICATOR","display_name":"ANALYSIS OF ROUND OFF ERRORS WITH REVERSIBILITY TEST AS A DYNAMICAL INDICATOR","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W2160884680","doi":"https://doi.org/10.1142/s021812741250215x","mag":"2160884680"},"language":"en","primary_location":{"id":"doi:10.1142/s021812741250215x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741250215x","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/1205.3060","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106225000","display_name":"Davide Faranda","orcid":"https://orcid.org/0000-0001-5001-5698"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I4210087306","display_name":"Laboratoire de M\u00e9t\u00e9orologie Dynamique","ror":"https://ror.org/000ehr937","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I142631665","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210087306","https://openalex.org/I4210145102","https://openalex.org/I4210145102","https://openalex.org/I4210148025"]},{"id":"https://openalex.org/I4210124937","display_name":"Laboratoire des Sciences du Climat et de l'Environnement","ror":"https://ror.org/03dsd0g48","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I195731000","https://openalex.org/I2738703131","https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210113668","https://openalex.org/I4210124937","https://openalex.org/I4210148025"]},{"id":"https://openalex.org/I4210161256","display_name":"Impact","ror":"https://ror.org/05d9dsr70","country_code":"CA","type":"nonprofit","lineage":["https://openalex.org/I4210161256"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["CA","DE","FR","IT"],"is_corresponding":false,"raw_author_name":"DAVIDE FARANDA","raw_affiliation_strings":["Department of Physics, University of Bologna, Via Irnerio 46, Bologna 40126, Italy","Extr\u00e8mes : Statistiques, Impacts et R\u00e9gionalisation","University of Hamburg","Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]","Laboratoire de M\u00e9t\u00e9orologie Dynamique (UMR 8539)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Bologna, Via Irnerio 46, Bologna 40126, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"Extr\u00e8mes : Statistiques, Impacts et R\u00e9gionalisation","institution_ids":["https://openalex.org/I4210161256"]},{"raw_affiliation_string":"University of Hamburg","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]","institution_ids":["https://openalex.org/I4210124937"]},{"raw_affiliation_string":"Laboratoire de M\u00e9t\u00e9orologie Dynamique (UMR 8539)","institution_ids":["https://openalex.org/I4210087306"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059679080","display_name":"Mart\u00edn F. Mestre","orcid":"https://orcid.org/0009-0001-9329-5260"},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I4210109836","display_name":"Instituto de F\u00edsica La Plata","ror":"https://ror.org/01pmtm379","country_code":"AR","type":"facility","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210109836","https://openalex.org/I4210123736","https://openalex.org/I4210138160","https://openalex.org/I4387155568","https://openalex.org/I874386039"]},{"id":"https://openalex.org/I874386039","display_name":"Universidad Nacional de La Plata","ror":"https://ror.org/01tjs6929","country_code":"AR","type":"education","lineage":["https://openalex.org/I874386039"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"MART\u00cdN FEDERICO MESTRE","raw_affiliation_strings":["Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astron\u00f3micas y Geof\u00edsicas, Universidad Nacional de La Plata, Instituto de Astrof\u00edsica de La Plata, (CCT La Plata \u2013 CONICET, UNLP), Paseo del Bosque S/N, La Plata 1900, Argentina","Instituto de F\u00edsica La Plata [La Plata]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astron\u00f3micas y Geof\u00edsicas, Universidad Nacional de La Plata, Instituto de Astrof\u00edsica de La Plata, (CCT La Plata \u2013 CONICET, UNLP), Paseo del Bosque S/N, La Plata 1900, Argentina","institution_ids":["https://openalex.org/I874386039","https://openalex.org/I151201029"]},{"raw_affiliation_string":"Instituto de F\u00edsica La Plata [La Plata]","institution_ids":["https://openalex.org/I4210109836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074144409","display_name":"G. Turchetti","orcid":null},"institutions":[{"id":"https://openalex.org/I4210148700","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Bologna","ror":"https://ror.org/04j0x0h93","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210148700"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"GIORGIO TURCHETTI","raw_affiliation_strings":["Department of Physics, University of Bologna, INFN-Bologna, Via Irnerio 46, Bologna 40126, Italy","Alma Mater Studiorum Universit\u00e0 di Bologna = University of Bologna"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Bologna, INFN-Bologna, Via Irnerio 46, Bologna 40126, Italy","institution_ids":["https://openalex.org/I4210148700","https://openalex.org/I9360294"]},{"raw_affiliation_string":"Alma Mater Studiorum Universit\u00e0 di Bologna = University of Bologna","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9426,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.86521967,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"09","first_page":"1250215","last_page":"1250215"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9965000152587891,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9735999703407288,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7722427845001221},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.7045495510101318},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.6793174743652344},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.6354197263717651},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.6301698684692383},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6267191171646118},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5728937983512878},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5570498704910278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5500196814537048},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5082187652587891},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5069403648376465},{"id":"https://openalex.org/keywords/standard-map","display_name":"Standard map","score":0.48821666836738586},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.48094600439071655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3017224073410034},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2892446517944336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14928776025772095},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14241454005241394},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09543922543525696}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7722427845001221},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7045495510101318},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.6793174743652344},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.6354197263717651},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.6301698684692383},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6267191171646118},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5728937983512878},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5570498704910278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5500196814537048},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5082187652587891},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5069403648376465},{"id":"https://openalex.org/C82229145","wikidata":"https://www.wikidata.org/wiki/Q2257676","display_name":"Standard map","level":3,"score":0.48821666836738586},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.48094600439071655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3017224073410034},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2892446517944336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14928776025772095},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14241454005241394},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09543922543525696},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1142/s021812741250215x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741250215x","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:1205.3060","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.3060","pdf_url":"https://arxiv.org/pdf/1205.3060","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:HAL:hal-02886318v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02886318","pdf_url":"https://hal.science/hal-02886318v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International journal of bifurcation and chaos in applied sciences and engineering , 2012, 22 (09), pp.1250215. &#x27E8;10.1142/S021812741250215X&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.760.811","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.760.811","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1205.3060.pdf","raw_type":"text"},{"id":"pmh:oai:ri.conicet.gov.ar:11336/82526","is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/82526","pdf_url":null,"source":{"id":"https://openalex.org/S4306401400","display_name":"Conicet","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210104196","host_organization_name":"Centro Cient\u00edfico Tecnol\u00f3gico - Nordeste","host_organization_lineage":["https://openalex.org/I4210104196"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:sedici.unlp.edu.ar:10915/129367","is_oa":false,"landing_page_url":"http://sedici.unlp.edu.ar/handle/10915/129367","pdf_url":null,"source":{"id":"https://openalex.org/S4306400803","display_name":"El Servicio de Difusi\u00f3n de la Creaci\u00f3n Intelectual (National University of La Plata)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I874386039","host_organization_name":"Universidad Nacional de La Plata","host_organization_lineage":["https://openalex.org/I874386039"],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1205.3060","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.3060","pdf_url":"https://arxiv.org/pdf/1205.3060","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321594","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59"},{"id":"https://openalex.org/F4320323553","display_name":"Universit\u00e0 di Bologna","ror":"https://ror.org/01111rn36"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W53949467","https://openalex.org/W1968536505","https://openalex.org/W1980372148","https://openalex.org/W1991978029","https://openalex.org/W1992120986","https://openalex.org/W1992203513","https://openalex.org/W1994836995","https://openalex.org/W2000050403","https://openalex.org/W2032874293","https://openalex.org/W2039100300","https://openalex.org/W2053392159","https://openalex.org/W2057001158","https://openalex.org/W2057276798","https://openalex.org/W2069006672","https://openalex.org/W2070235235","https://openalex.org/W2072998188","https://openalex.org/W2081817659","https://openalex.org/W2082471253","https://openalex.org/W2104251500","https://openalex.org/W2123548217","https://openalex.org/W2124428761","https://openalex.org/W2127143993","https://openalex.org/W2135425748","https://openalex.org/W2143439529","https://openalex.org/W2152254020","https://openalex.org/W2168862801","https://openalex.org/W2169004268","https://openalex.org/W2752061190","https://openalex.org/W2951816919","https://openalex.org/W3099246320"],"related_works":["https://openalex.org/W2973136064","https://openalex.org/W2046468556","https://openalex.org/W2012691558","https://openalex.org/W1985724481","https://openalex.org/W2009385573","https://openalex.org/W4302160352","https://openalex.org/W1990019600","https://openalex.org/W1992333303","https://openalex.org/W1489032209","https://openalex.org/W598862700"],"abstract_inverted_index":{"We":[0],"compare":[1],"the":[2,7,22,25,33,49,52,64,67,92,96,106,113,120,124,129,132,136,141,147,155,173,180,189,197,211,214,220],"divergence":[3,138],"of":[4,24,35,39,51,66,76,85,98,108,115,144,185,213],"orbits":[5,110,187],"and":[6,135,188,201],"reversibility":[8,53,133],"error":[9,27,134],"for":[10,42,82,123,140],"discrete":[11],"time":[12,175],"dynamical":[13,72,157,165],"systems.":[14],"These":[15],"two":[16],"quantities":[17],"are":[18,103,127,225],"used":[19],"to":[20,112],"explore":[21],"behavior":[23],"global":[26],"induced":[28,78],"by":[29,79],"round":[30,80,116],"off":[31,81,117],"in":[32,95,105],"computation":[34,56],"orbits.":[36],"The":[37,74],"similarity":[38],"results":[40,93,121],"found":[41],"any":[43],"system":[44],"we":[45],"have":[46],"analyzed":[47],"suggests":[48],"use":[50],"error,":[54,118],"whose":[55],"is":[57,204],"straightforward":[58],"since":[59],"it":[60],"does":[61],"not":[62],"require":[63],"knowledge":[65],"exact":[68],"orbit,":[69],"as":[70,172,217,219],"a":[71,160],"indicator.":[73],"statistics":[75],"fluctuations":[77],"an":[83,152],"ensemble":[84],"initial":[86],"conditions":[87],"has":[88],"been":[89],"compared":[90],"with":[91,159,163],"obtained":[94,122],"case":[97,107,126],"random":[99],"perturbations.":[100],"Significant":[101],"differences":[102],"observed":[104],"regular":[109,200],"due":[111],"correlations":[114],"whereas":[119],"chaotic":[125,202,223],"nearly":[128],"same.":[130],"Both":[131],"orbit":[137],"computed":[139],"same":[142],"number":[143],"iterations":[145],"on":[146,154,168],"whole":[148],"phase":[149],"space":[150],"provide":[151],"insight":[153],"local":[156],"properties":[158],"detail":[161],"comparable":[162],"other":[164],"indicators":[166],"based":[167],"variational":[169],"methods":[170],"such":[171],"finite":[174],"maximum":[176],"Lyapunov":[177],"characteristic":[178],"exponent,":[179],"mean":[181],"exponential":[182],"growth":[183],"factor":[184],"nearby":[186,221],"smaller":[190],"alignment":[191],"index.":[192],"For":[193,207],"2D":[194],"symplectic":[195,209],"maps,":[196,210],"differentiation":[198],"between":[199],"regions":[203,224],"well":[205,218],"full-filled.":[206],"4D":[208],"structure":[212],"resonance":[215],"web":[216],"weakly":[222],"accurately":[226],"described.":[227]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-12T08:23:45.883708","created_date":"2025-10-10T00:00:00"}
