{"id":"https://openalex.org/W3033074347","doi":"https://doi.org/10.1137/19m1289959","title":"Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle","display_name":"Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3033074347","doi":"https://doi.org/10.1137/19m1289959","mag":"3033074347"},"language":"en","primary_location":{"id":"doi:10.1137/19m1289959","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1289959","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1910.01954","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Douglas D. Novaes","orcid":"https://orcid.org/0000-0002-9147-8442"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Douglas D. Novaes","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9147-8442","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Tere M. Seara","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tere M. Seara","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Marco A. Teixeira","orcid":"https://orcid.org/0000-0002-5386-9282"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marco A. Teixeira","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5386-9282","affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Iris O. Zeli","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iris O. Zeli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.128,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.75551431,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"2","first_page":"1343","last_page":"1371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9692999720573425,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9692999720573425,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.010700000450015068,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.0031999999191612005,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.7506999969482422},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7396000027656555},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.70169997215271},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6685000061988831},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6416000127792358},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6273999810218811},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6053000092506409},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5099999904632568},{"id":"https://openalex.org/keywords/quasi-periodic","display_name":"Quasi periodic","score":0.424699991941452},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.40230000019073486}],"concepts":[{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.7506999969482422},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7396000027656555},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.70169997215271},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6685000061988831},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.652899980545044},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6416000127792358},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6337000131607056},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6273999810218811},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6053000092506409},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5099999904632568},{"id":"https://openalex.org/C3019213175","wikidata":"https://www.wikidata.org/wiki/Q7269515","display_name":"Quasi periodic","level":2,"score":0.424699991941452},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C120241303","wikidata":"https://www.wikidata.org/wiki/Q3503302","display_name":"Periodic sequence","level":2,"score":0.3878999948501587},{"id":"https://openalex.org/C2989467761","wikidata":"https://www.wikidata.org/wiki/Q10693","display_name":"Periodic system","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3522000014781952},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32749998569488525},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31189998984336853},{"id":"https://openalex.org/C171912257","wikidata":"https://www.wikidata.org/wiki/Q11019","display_name":"Mechanical system","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C207769094","wikidata":"https://www.wikidata.org/wiki/Q4245771","display_name":"Singularity theory","level":3,"score":0.30309998989105225},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2662999927997589},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.26109999418258667},{"id":"https://openalex.org/C76379757","wikidata":"https://www.wikidata.org/wiki/Q2902561","display_name":"Separatrix","level":3,"score":0.2531999945640564},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.2513999938964844}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/19m1289959","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1289959","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"},{"id":"pmh:oai:arXiv.org:1910.01954","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.01954","pdf_url":"https://arxiv.org/pdf/1910.01954","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:upcommons.upc.edu:2117/329583","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1910.01954","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:dnet:upcommonspor::ad94ddf5001a697a2d4b5da702973777","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/329583","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/submittedVersion"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1910.01954","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.01954","pdf_url":"https://arxiv.org/pdf/1910.01954","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":[{"id":"https://openalex.org/G1308037761","display_name":null,"funder_award_id":"2013/21078-8","funder_id":"https://openalex.org/F4320323207","funder_display_name":"Funda\u00e7\u00e3o Amaz\u00f4nia Paraense de Amparo \u00e0 Pesquisa"},{"id":"https://openalex.org/G1556589347","display_name":null,"funder_award_id":"2017SGR1049","funder_id":"https://openalex.org/F4320321506","funder_display_name":"Consell Catal\u00e0 de Recerca i Innovaci\u00f3"},{"id":"https://openalex.org/G1951737086","display_name":null,"funder_award_id":"306649/2018-7","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G202495085","display_name":null,"funder_award_id":"1440140","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G295657101","display_name":null,"funder_award_id":"2019/","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G318376798","display_name":null,"funder_award_id":"438975/ 2018-9","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3683489966","display_name":null,"funder_award_id":"2019/10269-3","funder_id":"https://openalex.org/F4320323207","funder_display_name":"Funda\u00e7\u00e3o Amaz\u00f4nia Paraense de Amparo \u00e0 Pesquisa"},{"id":"https://openalex.org/G4402292705","display_name":null,"funder_award_id":"DMS-1440140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4456229148","display_name":null,"funder_award_id":"2018/16430-8","funder_id":"https://openalex.org/F4320323207","funder_display_name":"Funda\u00e7\u00e3o Amaz\u00f4nia Paraense de Amparo \u00e0 Pesquisa"},{"id":"https://openalex.org/G5364454070","display_name":null,"funder_award_id":"438975/2018-9","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5513212909","display_name":null,"funder_award_id":"438975/ 2018-9","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G5522687857","display_name":null,"funder_award_id":"PGC2018-098676-B-100","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5969482202","display_name":null,"funder_award_id":"DMS-1440140","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6091058458","display_name":null,"funder_award_id":"2018/ 13481-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G615524401","display_name":null,"funder_award_id":"2019/10269-3","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G6293298625","display_name":null,"funder_award_id":"2018/13481-0","funder_id":"https://openalex.org/F4320323207","funder_display_name":"Funda\u00e7\u00e3o Amaz\u00f4nia Paraense de Amparo \u00e0 Pesquisa"},{"id":"https://openalex.org/G6846924553","display_name":null,"funder_award_id":"306649/2018-7","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G7861063861","display_name":null,"funder_award_id":"2018/16430-8","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G811546825","display_name":"Mathematical Sciences Research Institute (MSRI)","funder_award_id":"1440140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8256299936","display_name":null,"funder_award_id":"PGC2018-098676-B-100","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G8510388149","display_name":null,"funder_award_id":"2018/16430-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8593099097","display_name":null,"funder_award_id":"2019/10269-3","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G8642496912","display_name":null,"funder_award_id":"2018/ 13481-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320321506","display_name":"Consell Catal\u00e0 de Recerca i Innovaci\u00f3","ror":null},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"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/F4320322121","display_name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats","ror":"https://ror.org/0371hy230"},{"id":"https://openalex.org/F4320323207","display_name":"Funda\u00e7\u00e3o Amaz\u00f4nia Paraense de Amparo \u00e0 Pesquisa","ror":"https://ror.org/00ssgrj25"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1772140372","https://openalex.org/W1850403730","https://openalex.org/W1963488314","https://openalex.org/W1973538380","https://openalex.org/W1977848563","https://openalex.org/W2001672492","https://openalex.org/W2013210442","https://openalex.org/W2013501206","https://openalex.org/W2016767879","https://openalex.org/W2019143828","https://openalex.org/W2041192585","https://openalex.org/W2047449028","https://openalex.org/W2053758441","https://openalex.org/W2068728923","https://openalex.org/W2080890623","https://openalex.org/W2089466166","https://openalex.org/W2223722977","https://openalex.org/W2493008392","https://openalex.org/W2519658861","https://openalex.org/W2750473404","https://openalex.org/W2778531943","https://openalex.org/W2890663667","https://openalex.org/W2894718329","https://openalex.org/W2999471114"],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1,89],"the":[2,29,59,82],"existence":[3],"of":[4,10,19,90],"periodic":[5,17,66],"solutions":[6],"in":[7],"a":[8,33,41,45,88,91],"class":[9],"planar":[11],"Filippov":[12],"systems":[13],"obtained":[14],"from":[15,81],"non-autonomous":[16],"perturbations":[18],"reversible":[20],"piecewise":[21,93],"smooth":[22],"differential":[23],"systems.":[24],"It":[25,51],"is":[26,38,52,96],"assumed":[27],"that":[28,54],"unperturbed":[30],"system":[31,61],"presents":[32],"simple":[34],"twofold":[35,47],"cycle,":[36],"which":[37],"characterized":[39],"by":[40],"closed":[42],"trajectory":[43],"connecting":[44],"visible":[46],"singularity":[48],"to":[49,70],"itself.":[50],"shown":[53],"under":[55],"certain":[56],"generic":[57],"conditions":[58],"perturbed":[60,92],"has":[62],"sliding":[63],"and":[64],"crossing":[65],"solutions.":[67],"In":[68],"order":[69],"get":[71],"our":[72],"results,":[73],"Melnikov's":[74],"ideas":[75],"are":[76],"applied":[77],"together":[78],"with":[79],"tools":[80],"geometric":[83],"singular":[84],"perturbation":[85],"theory.":[86],"Finally,":[87],"Hamiltonian":[94],"model":[95],"performed.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2020-06-12T00:00:00"}