{"id":"https://openalex.org/W2018228150","doi":"https://doi.org/10.1080/10586458.2005.10128923","title":"The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards","display_name":"The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2018228150","doi":"https://doi.org/10.1080/10586458.2005.10128923","mag":"2018228150"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2005.10128923","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2005.10128923","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":["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/A5041678545","display_name":"Sylvie Oliffson Kamphorst","orcid":"https://orcid.org/0000-0002-1185-5499"},"institutions":[{"id":"https://openalex.org/I4210158408","display_name":"Matrix Research (United States)","ror":"https://ror.org/04mw0p229","country_code":"US","type":"company","lineage":["https://openalex.org/I4210158408"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sylvie Oliffson Kamphorst","raw_affiliation_strings":["\n Departamento de Matem\u00e1tica ICEx UFMG, Caixa Postal 702, 30123-970 Brazil","Departamento de Matem\u00e1tica ICEx UFMG, Caixa Postal 702, 30123-970 Brazil"],"affiliations":[{"raw_affiliation_string":"\n Departamento de Matem\u00e1tica ICEx UFMG, Caixa Postal 702, 30123-970 Brazil","institution_ids":["https://openalex.org/I4210158408"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica ICEx UFMG, Caixa Postal 702, 30123-970 Brazil","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086380263","display_name":"S\u00f4nia Pinto-de-Carvalho","orcid":"https://orcid.org/0000-0002-4270-4220"},"institutions":[{"id":"https://openalex.org/I4210158408","display_name":"Matrix Research (United States)","ror":"https://ror.org/04mw0p229","country_code":"US","type":"company","lineage":["https://openalex.org/I4210158408"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S\u00f4nia Pinto-de-Carvalho","raw_affiliation_strings":["\n Departamento de Matem\u00e1tica ICEx UFMG, Caixa Postal 702, 30123-970 Brazil","Departamento de Matem\u00e1tica ICEx UFMG, Caixa Postal 702, 30123-970 Brazil"],"affiliations":[{"raw_affiliation_string":"\n Departamento de Matem\u00e1tica ICEx UFMG, Caixa Postal 702, 30123-970 Brazil","institution_ids":["https://openalex.org/I4210158408"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica ICEx UFMG, Caixa Postal 702, 30123-970 Brazil","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041678545"],"corresponding_institution_ids":["https://openalex.org/I4210158408"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.1311324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"3","first_page":"299","last_page":"306"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9983999729156494,"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":0.9818999767303467,"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/mathematics","display_name":"Mathematics","score":0.8695980310440063},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.7278462648391724},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6775810718536377},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.49646908044815063},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.47004976868629456},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4568430185317993},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42130327224731445},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37577158212661743},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12982922792434692},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04996359348297119},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0494614839553833}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8695980310440063},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7278462648391724},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6775810718536377},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.49646908044815063},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.47004976868629456},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4568430185317993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42130327224731445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37577158212661743},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12982922792434692},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04996359348297119},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0494614839553833},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2005.10128923","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2005.10128923","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:CULeuclid:euclid.em/1128371755","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1128371755","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.5212","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.5212","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/nlin/0410019v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322980","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","ror":"https://ror.org/00nc55f03"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W579126278","https://openalex.org/W606515989","https://openalex.org/W1503553685","https://openalex.org/W1524565983","https://openalex.org/W1612323916","https://openalex.org/W2008962126","https://openalex.org/W2010318084","https://openalex.org/W2012127433","https://openalex.org/W2018651156","https://openalex.org/W2042963108","https://openalex.org/W2059718794","https://openalex.org/W2081817659"],"related_works":["https://openalex.org/W3144804801","https://openalex.org/W4292014234","https://openalex.org/W122314361","https://openalex.org/W2348288500","https://openalex.org/W4287115018","https://openalex.org/W3175984101","https://openalex.org/W2038879066","https://openalex.org/W2597178793","https://openalex.org/W2951014123","https://openalex.org/W4293097192"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3],"address":[4],"the":[5,9,36,50,58,62],"question":[6],"of":[7,11,23,38,49],"proving":[8],"stability":[10,39],"elliptic":[12],"2-periodic":[13],"orbits":[14],"for":[15,65],"strictly":[16,66],"convex":[17,67],"billiards.":[18,68],"Eventhough":[19],"it":[20],"is":[21],"part":[22],"a":[24,47],"widely":[25],"accepted":[26],"belief":[27],"that":[28,35],"ellipticity":[29],"implies":[30],"stability,":[31],"classical":[32],"theorems":[33,55],"show":[34],"certainty":[37],"relies":[40],"upon":[41],"more":[42],"fine":[43],"conditions.":[44],"We":[45],"present":[46],"review":[48],"main":[51],"results":[52],"and":[53,56],"general":[54],"describe":[57],"procedure":[59],"to":[60],"fullfill":[61],"supplementary":[63],"conditions":[64],"1":[69]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
