{"id":"https://openalex.org/W2954501257","doi":"https://doi.org/10.1142/s0218127419500998","title":"On the Topology of Isochronous Centers of Hamiltonian Differential Systems","display_name":"On the Topology of Isochronous Centers of Hamiltonian Differential Systems","publication_year":2019,"publication_date":"2019-06-15","ids":{"openalex":"https://openalex.org/W2954501257","doi":"https://doi.org/10.1142/s0218127419500998","mag":"2954501257"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419500998","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127419500998","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127419500998","source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127419500998","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007403356","display_name":"Guangfeng Dong","orcid":"https://orcid.org/0000-0001-5581-494X"},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guangfeng Dong","raw_affiliation_strings":["Department of Mathematics, Jinan University, Guangzhou 510632, P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-5581-494X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jinan University, Guangzhou 510632, P. R. China","institution_ids":["https://openalex.org/I159948400"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033679688","display_name":"Changjian Liu","orcid":"https://orcid.org/0000-0001-8631-3398"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changjian Liu","raw_affiliation_strings":["School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai 519082, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai 519082, P. R. China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025872255","display_name":"Jiazhong Yang","orcid":"https://orcid.org/0000-0002-6046-2157"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiazhong Yang","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007403356"],"corresponding_institution_ids":["https://openalex.org/I159948400"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.15313936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"29","issue":"06","first_page":"1950099","last_page":"1950099"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9251000285148621,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.909500002861023,"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":0.6454169750213623},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5821653604507446},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5569319725036621},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44919702410697937},{"id":"https://openalex.org/keywords/riemann-surface","display_name":"Riemann surface","score":0.43267661333084106},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.42776787281036377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.317315936088562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20599088072776794}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6454169750213623},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5821653604507446},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5569319725036621},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44919702410697937},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.43267661333084106},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.42776787281036377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.317315936088562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20599088072776794},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127419500998","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127419500998","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127419500998","source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1142/s0218127419500998","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127419500998","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127419500998","source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2009120433","display_name":null,"funder_award_id":"11771315","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2045309974","display_name":null,"funder_award_id":"11671016","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7737508804","display_name":null,"funder_award_id":"2017A030310181","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G8377663395","display_name":null,"funder_award_id":"11701217","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null},{"id":"https://openalex.org/F4320322292","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2954501257.pdf","grobid_xml":"https://content.openalex.org/works/W2954501257.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W389472000","https://openalex.org/W1495980450","https://openalex.org/W1982186107","https://openalex.org/W2003049656","https://openalex.org/W2013777138","https://openalex.org/W2018313706","https://openalex.org/W2025529056","https://openalex.org/W2027048439","https://openalex.org/W2043442376","https://openalex.org/W2048682806","https://openalex.org/W2051346103","https://openalex.org/W2056854432","https://openalex.org/W2058696474","https://openalex.org/W2074243047","https://openalex.org/W2083520964","https://openalex.org/W2090727745","https://openalex.org/W2573448240","https://openalex.org/W4206311976"],"related_works":["https://openalex.org/W2075972694","https://openalex.org/W4235543436","https://openalex.org/W2024310106","https://openalex.org/W3103887416","https://openalex.org/W1983586807","https://openalex.org/W2146089235","https://openalex.org/W2032438873","https://openalex.org/W2017288407","https://openalex.org/W4238581249","https://openalex.org/W2952228942"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2,98],"we":[3,111,152],"study":[4,153],"the":[5,23,28,38,43,47,57,91,97,154,172],"topology":[6],"of":[7,10,42,51,60,77,87,90,116,123,126,134,143],"isochronous":[8,24,62,117],"centers":[9,118],"Hamiltonian":[11,16,124,158],"differential":[12],"systems":[13,125,159],"with":[14,141,160],"polynomial":[15],"functions":[17],"[Formula:":[18,31,54,100,107,128,136,147],"see":[19,32,55,101,108,129,137,148],"text]":[20,102,138],"such":[21,74],"that":[22,75],"center":[25,63],"lies":[26],"on":[27],"level":[29,52],"curve":[30,53],"text].":[33,109,149],"We":[34],"prove":[35],"that,":[36],"in":[37,96],"one-dimensional":[39],"homology":[40],"group":[41],"Riemann":[44],"surface":[45],"(removing":[46],"points":[48],"at":[49,81,85],"infinity)":[50],"text],":[56,130],"vanishing":[58],"cycle":[59],"an":[61],"cannot":[64],"belong":[65],"to":[66,106,169],"a":[67,82,120],"subgroup":[68],"generated":[69],"by":[70,171],"those":[71],"small":[72],"loops":[73],"each":[76],"them":[78],"is":[79,103],"centered":[80],"removed":[83],"point":[84],"infinity":[86],"having":[88],"one":[89],"two":[92],"special":[93],"types":[94],"described":[95],"where":[99],"sufficiently":[104],"close":[105],"Besides,":[110],"present":[112],"some":[113,157],"topological":[114],"properties":[115],"for":[119,156],"large":[121],"class":[122],"degree":[127,135],"whose":[131],"homogeneous":[132],"parts":[133],"contain":[139],"factors":[140],"multiplicity":[142],"no":[144],"more":[145],"than":[146],"As":[150],"applications,":[151],"nonisochronicity":[155],"quite":[161],"complicated":[162],"forms":[163],"which":[164],"are":[165],"usually":[166],"very":[167],"hard":[168],"handle":[170],"classical":[173],"tools.":[174]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
