{"id":"https://openalex.org/W2524557565","doi":"https://doi.org/10.1080/10586458.2016.1226993","title":"On a Very Steep Version of the Standard Map","display_name":"On a Very Steep Version of the Standard Map","publication_year":2016,"publication_date":"2016-10-07","ids":{"openalex":"https://openalex.org/W2524557565","doi":"https://doi.org/10.1080/10586458.2016.1226993","mag":"2524557565"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2016.1226993","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2016.1226993","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1609.07424","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057723993","display_name":"Maxim Arnold","orcid":"https://orcid.org/0000-0002-4500-8394"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. Arnold","raw_affiliation_strings":["Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX, USA","institution_ids":["https://openalex.org/I162577319"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053411993","display_name":"Thomas Dauer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Dauer","raw_affiliation_strings":["Indiana University, Bloomington, IN, USA"],"affiliations":[{"raw_affiliation_string":"Indiana University, Bloomington, IN, USA","institution_ids":["https://openalex.org/I4210119109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014125907","display_name":"Meg Doucette","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Doucette","raw_affiliation_strings":["University of Chicago, Chicago, IL, USA"],"affiliations":[{"raw_affiliation_string":"University of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166","https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109339562","display_name":"S.-C. Wolf","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S.-C. Wolf","raw_affiliation_strings":["Cambridge University, Cambridge, UK"],"affiliations":[{"raw_affiliation_string":"Cambridge University, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057723993"],"corresponding_institution_ids":["https://openalex.org/I162577319"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10218819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"1","first_page":"93","last_page":"99"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9995999932289124,"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":0.9995999932289124,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10566","display_name":"Laser-Matter Interactions and Applications","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.8610888719558716},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7387747168540955},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7345110177993774},{"id":"https://openalex.org/keywords/standard-map","display_name":"Standard map","score":0.6456749439239502},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6007676124572754},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3653094172477722},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33639681339263916},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26891404390335083},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.066904217004776},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06503430008888245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8610888719558716},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7387747168540955},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7345110177993774},{"id":"https://openalex.org/C82229145","wikidata":"https://www.wikidata.org/wiki/Q2257676","display_name":"Standard map","level":3,"score":0.6456749439239502},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6007676124572754},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3653094172477722},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33639681339263916},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26891404390335083},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.066904217004776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06503430008888245},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.2016.1226993","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2016.1226993","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1609.07424","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.07424","pdf_url":"https://arxiv.org/pdf/1609.07424","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1609.07424","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.07424","pdf_url":"https://arxiv.org/pdf/1609.07424","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/F4320309070","display_name":"Brown University","ror":"https://ror.org/05gq02987"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1560884718","https://openalex.org/W2062908014","https://openalex.org/W2081911817","https://openalex.org/W2091064946","https://openalex.org/W2160163816","https://openalex.org/W2487330854","https://openalex.org/W3175367423","https://openalex.org/W4388288416"],"related_works":["https://openalex.org/W4300899577","https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W3013085049","https://openalex.org/W2551767278","https://openalex.org/W1560496689","https://openalex.org/W2000200567","https://openalex.org/W1973978937","https://openalex.org/W1992739770"],"abstract_inverted_index":{"We":[0,17],"consider":[1],"the":[2,6,9,13,26,43,47,56],"long-time":[3],"behavior":[4],"of":[5,8,12,23,36],"trajectories":[7,27,48],"discontinuous":[10],"analog":[11],"standard":[14],"Chirikov":[15],"map.":[16],"prove":[18],"that":[19],"for":[20,30,42,46,55],"some":[21],"values":[22],"parameters":[24,37],"all":[25,31],"remain":[28],"bounded":[29],"time.":[32],"For":[33],"other":[34],"set":[35],"we":[38],"provide":[39],"an":[40],"estimate":[41],"escape":[44,58],"rate":[45],"and":[49],"present":[50],"a":[51],"numerically":[52],"supported":[53],"conjecture":[54],"actual":[57],"rate.":[59]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}