{"id":"https://openalex.org/W4303699772","doi":"https://doi.org/10.3390/e24101427","title":"Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well","display_name":"Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well","publication_year":2022,"publication_date":"2022-10-07","ids":{"openalex":"https://openalex.org/W4303699772","doi":"https://doi.org/10.3390/e24101427","pmid":"https://pubmed.ncbi.nlm.nih.gov/37420447"},"language":"en","primary_location":{"id":"doi:10.3390/e24101427","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24101427","pdf_url":"https://www.mdpi.com/1099-4300/24/10/1427/pdf?version=1665729542","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/10/1427/pdf?version=1665729542","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084823587","display_name":"Fl\u00e1vio Heleno Graciano","orcid":"https://orcid.org/0000-0003-3906-8267"},"institutions":[{"id":"https://openalex.org/I4210102163","display_name":"Instituto Federal do Sul de Minas","ror":"https://ror.org/01drtms03","country_code":"BR","type":"education","lineage":["https://openalex.org/I4210102163"]},{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Fl\u00e1vio Heleno Graciano","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual Paulista (UNESP), Instituto de Geoci\u00eancias e Ci\u00eancias Exatas, C\u00e2mpus de Rio Claro, Av. 24A, 1515, S\u00e3o Paulo 13506-900, SP, Brazil","Instituto Federal do Sul de Minas Gerais (IFSULDEMINAS), Campus Pouso Alegre, Avenida Maria da Concei\u00e7\u00e3o Santos n\u00ba 900, Bairro Parque Real, Pouso Alegre 37560-260, MG, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-3906-8267","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual Paulista (UNESP), Instituto de Geoci\u00eancias e Ci\u00eancias Exatas, C\u00e2mpus de Rio Claro, Av. 24A, 1515, S\u00e3o Paulo 13506-900, SP, Brazil","institution_ids":["https://openalex.org/I879563668"]},{"raw_affiliation_string":"Instituto Federal do Sul de Minas Gerais (IFSULDEMINAS), Campus Pouso Alegre, Avenida Maria da Concei\u00e7\u00e3o Santos n\u00ba 900, Bairro Parque Real, Pouso Alegre 37560-260, MG, Brazil","institution_ids":["https://openalex.org/I4210102163"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013020198","display_name":"Diogo Ricardo da Costa","orcid":"https://orcid.org/0000-0003-1891-6415"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]},{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Diogo Ricardo da Costa","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual Paulista (UNESP), Instituto de Geoci\u00eancias e Ci\u00eancias Exatas, C\u00e2mpus de Rio Claro, Av. 24A, 1515, S\u00e3o Paulo 13506-900, SP, Brazil","Departamento de F\u00edsica, Universidade Federal do Paran\u00e1 (UFPR), Curitiba 80060-000, PR, Brazil","Instituto de Matem\u00e1tica e Estat\u00edstica da Universidade de S\u00e3o Paulo (IME-USP), Rua do Mat\u00e3o, 1010, S\u00e3o Paulo 05508-090, SP, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual Paulista (UNESP), Instituto de Geoci\u00eancias e Ci\u00eancias Exatas, C\u00e2mpus de Rio Claro, Av. 24A, 1515, S\u00e3o Paulo 13506-900, SP, Brazil","institution_ids":["https://openalex.org/I879563668"]},{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Federal do Paran\u00e1 (UFPR), Curitiba 80060-000, PR, Brazil","institution_ids":["https://openalex.org/I52418104"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica da Universidade de S\u00e3o Paulo (IME-USP), Rua do Mat\u00e3o, 1010, S\u00e3o Paulo 05508-090, SP, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039263680","display_name":"Edson D. Leonel","orcid":"https://orcid.org/0000-0001-8224-3329"},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Edson D. Leonel","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual Paulista (UNESP), Instituto de Geoci\u00eancias e Ci\u00eancias Exatas, C\u00e2mpus de Rio Claro, Av. 24A, 1515, S\u00e3o Paulo 13506-900, SP, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual Paulista (UNESP), Instituto de Geoci\u00eancias e Ci\u00eancias Exatas, C\u00e2mpus de Rio Claro, Av. 24A, 1515, S\u00e3o Paulo 13506-900, SP, Brazil","institution_ids":["https://openalex.org/I879563668"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047675569","display_name":"Juliano A. de Oliveira","orcid":"https://orcid.org/0000-0001-7238-4777"},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Juliano A. de Oliveira","raw_affiliation_strings":["C\u00e2mpus de S\u00e3o Jo\u00e3o da Boa Vista, Universidade Estadual Paulista, Av. Profa. Isette Corr\u00eaa Font\u00e3o, 505, S\u00e3o Paulo 13876-750, SP, Brazil","Departamento de F\u00edsica, Universidade Estadual Paulista (UNESP), Instituto de Geoci\u00eancias e Ci\u00eancias Exatas, C\u00e2mpus de Rio Claro, Av. 24A, 1515, S\u00e3o Paulo 13506-900, SP, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-7238-4777","affiliations":[{"raw_affiliation_string":"C\u00e2mpus de S\u00e3o Jo\u00e3o da Boa Vista, Universidade Estadual Paulista, Av. Profa. Isette Corr\u00eaa Font\u00e3o, 505, S\u00e3o Paulo 13876-750, SP, Brazil","institution_ids":[]},{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual Paulista (UNESP), Instituto de Geoci\u00eancias e Ci\u00eancias Exatas, C\u00e2mpus de Rio Claro, Av. 24A, 1515, S\u00e3o Paulo 13506-900, SP, Brazil","institution_ids":["https://openalex.org/I879563668"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5047675569"],"corresponding_institution_ids":["https://openalex.org/I879563668"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1251,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.43673953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"24","issue":"10","first_page":"1427","last_page":"1427"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9993000030517578,"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":0.9993000030517578,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11575","display_name":"Nonlinear Photonic Systems","score":0.986299991607666,"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/nonlinear-system","display_name":"Nonlinear system","score":0.5766202211380005},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5764651298522949},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.5506198406219482},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5277743339538574},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5222383737564087},{"id":"https://openalex.org/keywords/phase-plane","display_name":"Phase plane","score":0.5017502307891846},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.47808241844177246},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.47606438398361206},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47333794832229614},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4639330506324768},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.4515867829322815},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4504087269306183},{"id":"https://openalex.org/keywords/particle","display_name":"Particle (ecology)","score":0.4289044141769409},{"id":"https://openalex.org/keywords/spacetime","display_name":"Spacetime","score":0.41072097420692444},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3718906044960022},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21479582786560059},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.1470281481742859},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1390966773033142},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08914726972579956},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.07745999097824097}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5766202211380005},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5764651298522949},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5506198406219482},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5277743339538574},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5222383737564087},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.5017502307891846},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.47808241844177246},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.47606438398361206},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47333794832229614},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4639330506324768},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.4515867829322815},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4504087269306183},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.4289044141769409},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.41072097420692444},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3718906044960022},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21479582786560059},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1470281481742859},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1390966773033142},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08914726972579956},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07745999097824097},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e24101427","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24101427","pdf_url":"https://www.mdpi.com/1099-4300/24/10/1427/pdf?version=1665729542","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:37420447","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37420447","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:3dff56beb1714b77b51fff0062fff5b8","is_oa":true,"landing_page_url":"https://doaj.org/article/3dff56beb1714b77b51fff0062fff5b8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 10, p 1427 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/10/1427/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24101427","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 10; Pages: 1427","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9602288","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9602288","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:repositorio.unesp.br:11449/247791","is_oa":true,"landing_page_url":"http://doi.org/10.3390/e24101427","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UNESP","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/e24101427","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24101427","pdf_url":"https://www.mdpi.com/1099-4300/24/10/1427/pdf?version=1665729542","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8600000143051147,"display_name":"Life below water","id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4303699772.pdf","grobid_xml":"https://content.openalex.org/works/W4303699772.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W337816440","https://openalex.org/W1508348648","https://openalex.org/W1551533685","https://openalex.org/W1613181396","https://openalex.org/W1980231281","https://openalex.org/W2024275187","https://openalex.org/W2028172717","https://openalex.org/W2036429825","https://openalex.org/W2039966934","https://openalex.org/W2044335626","https://openalex.org/W2046807849","https://openalex.org/W2047430603","https://openalex.org/W2051366848","https://openalex.org/W2053859329","https://openalex.org/W2056979893","https://openalex.org/W2066116321","https://openalex.org/W2067887541","https://openalex.org/W2070201361","https://openalex.org/W2088044678","https://openalex.org/W2092472312","https://openalex.org/W2095245485","https://openalex.org/W2103035375","https://openalex.org/W2738966399","https://openalex.org/W2748278404","https://openalex.org/W2907223503","https://openalex.org/W2957463244","https://openalex.org/W3044754695","https://openalex.org/W3098617939","https://openalex.org/W4230237964"],"related_works":["https://openalex.org/W2004708907","https://openalex.org/W2377429601","https://openalex.org/W2607684300","https://openalex.org/W2386043911","https://openalex.org/W3171270255","https://openalex.org/W2368252804","https://openalex.org/W2379367191","https://openalex.org/W2027776969","https://openalex.org/W2374427492","https://openalex.org/W2069167073"],"abstract_inverted_index":{"We":[0,39,57,73,125],"study":[1,74,86],"the":[2,27,35,41,59,75,78,107,135,142,154],"dynamics":[3,14],"of":[4,15,34,77],"classical":[5],"particles":[6],"confined":[7],"in":[8,129,153],"a":[9,21,67,82,98],"time-dependent":[10],"potential":[11,108],"well.":[12,38],"The":[13],"each":[16],"particle":[17,99],"is":[18,111],"described":[19],"by":[20,157],"two-dimensional":[22],"nonlinear":[23],"discrete":[24],"mapping":[25],"for":[26],"variables":[28],"energy":[29,104,122],"en":[30],"and":[31,44,53,61,65,110],"phase":[32,42],"\u03d5n":[33],"periodic":[36,49],"moving":[37],"obtain":[40,71],"space":[43],"show":[45,127,148],"that":[46,151],"it":[47,119],"contains":[48],"islands,":[50],"chaotic":[51],"sea,":[52],"invariant":[54],"spanning":[55],"curves.":[56],"find":[58],"elliptic":[60],"hyperbolic":[62],"fixed":[63],"points":[64],"discuss":[66],"numerical":[68],"method":[69],"to":[70,105,123],"them.":[72],"dispersion":[76],"initial":[79],"conditions":[80],"after":[81],"single":[83],"iteration.":[84],"This":[85],"allows":[87],"finding":[88],"regions":[89,130],"where":[90],"multiple":[91,132],"reflections":[92,95,117],"occur.":[93],"Multiple":[94],"happen":[96],"when":[97,139],"does":[100],"not":[101],"have":[102],"enough":[103,121],"exit":[106],"well":[109],"trapped":[112],"inside":[113],"it,":[114],"suffering":[115],"several":[116],"until":[118],"has":[120],"exit.":[124],"also":[126],"deformations":[128],"with":[131],"reflection,":[133],"but":[134],"area":[136],"remains":[137],"constant":[138],"we":[140,147],"change":[141],"control":[143],"parameter":[144],"NC.":[145],"Finally,":[146],"some":[149],"structures":[150],"appear":[152],"e0e1":[155],"plane":[156],"using":[158],"density":[159],"plots.":[160]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}