{"id":"https://openalex.org/W4380741503","doi":"https://doi.org/10.1137/21m1450409","title":"Periodic Solutions, KAM Tori, and Bifurcations in the Planar Anisotropic Schwarzschild-Type Problem","display_name":"Periodic Solutions, KAM Tori, and Bifurcations in the Planar Anisotropic Schwarzschild-Type Problem","publication_year":2023,"publication_date":"2023-06-15","ids":{"openalex":"https://openalex.org/W4380741503","doi":"https://doi.org/10.1137/21m1450409"},"language":"en","primary_location":{"id":"doi:10.1137/21m1450409","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1450409","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","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/A5019853977","display_name":"\u00c2ngelo Alberti","orcid":"https://orcid.org/0000-0002-5991-4208"},"institutions":[{"id":"https://openalex.org/I190085865","display_name":"Universidade Federal de Sergipe","ror":"https://ror.org/028ka0n85","country_code":"BR","type":"education","lineage":["https://openalex.org/I190085865"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Angelo Alberti","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade Federal de Sergipe, Cidade Universit\u00e1ria Prof. Jos\u00e9 Alo\u00edsio de Campos, Jardim Rosa Elze, S\u00e3o Cristov\u00e3o-SE, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade Federal de Sergipe, Cidade Universit\u00e1ria Prof. Jos\u00e9 Alo\u00edsio de Campos, Jardim Rosa Elze, S\u00e3o Cristov\u00e3o-SE, Brazil","institution_ids":["https://openalex.org/I190085865"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026593361","display_name":"Cl\u00e1udio Vidal","orcid":"https://orcid.org/0000-0002-1630-0898"},"institutions":[{"id":"https://openalex.org/I221450849","display_name":"University of B\u00edo-B\u00edo","ror":"https://ror.org/04dndfk38","country_code":"CL","type":"education","lineage":["https://openalex.org/I221450849"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Claudio Vidal","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n, VIII Regi\u00f3n, Chile"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n, VIII Regi\u00f3n, Chile","institution_ids":["https://openalex.org/I221450849"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028413352","display_name":"J. Vidarte","orcid":"https://orcid.org/0000-0002-8218-9542"},"institutions":[{"id":"https://openalex.org/I38685851","display_name":"Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n","ror":"https://ror.org/03y6k2j68","country_code":"CL","type":"education","lineage":["https://openalex.org/I38685851"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Jhon Vidarte","raw_affiliation_strings":["Departamento de Matem\u00e1tica y F\u00edsica Aplicadas, Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n, Casilla 297, Concepci\u00f3n, Chile"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica y F\u00edsica Aplicadas, Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n, Casilla 297, Concepci\u00f3n, Chile","institution_ids":["https://openalex.org/I38685851"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019853977"],"corresponding_institution_ids":["https://openalex.org/I190085865"],"apc_list":null,"apc_paid":null,"fwci":0.1666,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.42744472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"22","issue":"2","first_page":"1053","last_page":"1075"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980999827384949,"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":0.9980999827384949,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9850999712944031,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/kolmogorov\u2013arnold\u2013moser-theorem","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","score":0.8733301162719727},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7380039095878601},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6961146593093872},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.648736298084259},{"id":"https://openalex.org/keywords/quasi-periodic","display_name":"Quasi periodic","score":0.5861386656761169},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5719307661056519},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5574359893798828},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.5282033085823059},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.5053723454475403},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.4989957809448242},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.45899561047554016},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.45586657524108887},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4405848979949951},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.43016350269317627},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3399221897125244},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.26341283321380615},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2578331232070923},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.235905259847641},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18162894248962402},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08700776100158691}],"concepts":[{"id":"https://openalex.org/C8522634","wikidata":"https://www.wikidata.org/wiki/Q587081","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","level":3,"score":0.8733301162719727},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7380039095878601},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6961146593093872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.648736298084259},{"id":"https://openalex.org/C3019213175","wikidata":"https://www.wikidata.org/wiki/Q7269515","display_name":"Quasi periodic","level":2,"score":0.5861386656761169},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5719307661056519},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5574359893798828},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.5282033085823059},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.5053723454475403},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.4989957809448242},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.45899561047554016},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.45586657524108887},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4405848979949951},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.43016350269317627},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3399221897125244},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.26341283321380615},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2578331232070923},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.235905259847641},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18162894248962402},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08700776100158691},{"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/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"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/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1450409","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1450409","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3862912604","display_name":null,"funder_award_id":"1220628","funder_id":"https://openalex.org/F4320338073","funder_display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320325372","display_name":"Universidad del B\u00edo-B\u00edo","ror":"https://ror.org/04dndfk38"},{"id":"https://openalex.org/F4320338073","display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","ror":"https://ror.org/02ap3w078"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1639543949","https://openalex.org/W1979076842","https://openalex.org/W1985080592","https://openalex.org/W1987524623","https://openalex.org/W2021496542","https://openalex.org/W2037834521","https://openalex.org/W2049576205","https://openalex.org/W2121511041","https://openalex.org/W2239582936","https://openalex.org/W2294351649","https://openalex.org/W2770630830","https://openalex.org/W3095826817","https://openalex.org/W4234926707","https://openalex.org/W4296477255"],"related_works":["https://openalex.org/W2260136577","https://openalex.org/W4388482631","https://openalex.org/W4299504254","https://openalex.org/W4292014234","https://openalex.org/W1954328068","https://openalex.org/W2033066703","https://openalex.org/W2034132653","https://openalex.org/W4385577794","https://openalex.org/W2803541738","https://openalex.org/W2900653290"],"abstract_inverted_index":{"We":[0,17],"investigate":[1],"analytically":[2],"the":[3,12,26,33,40,48,58,66],"existence":[4,59],"of":[5,8,28,30,35,42,47,60,65],"several":[6],"families":[7],"periodic":[9,37,51,61,67],"solutions":[10,52],"for":[11,32],"planar":[13],"anisotropic":[14],"Schwarzschild-type":[15],"problem.":[16],"use":[18],"reduction":[19],"and":[20],"averaging":[21],"theory,":[22],"as":[23,25],"well":[24],"technique":[27],"continuation":[29],"Poincar\u00e9,":[31],"study":[34],"symmetric":[36],"solutions.":[38,68],"Moreover,":[39],"determination":[41],"KAM":[43],"2-tori":[44],"encasing":[45],"some":[46],"linearly":[49],"stable":[50],"is":[53],"proved.":[54],"Finally,":[55],"we":[56],"analyze":[57],"Hamiltonian":[62],"pitchfork":[63],"bifurcation":[64]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}