{"id":"https://openalex.org/W1976645861","doi":"https://doi.org/10.1142/s0218127413500478","title":"THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A PERTURBATION OF HYPERELLIPTIC HAMILTONIAN SYSTEM WITH DEGENERATED POLYCYCLE","display_name":"THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A PERTURBATION OF HYPERELLIPTIC HAMILTONIAN SYSTEM WITH DEGENERATED POLYCYCLE","publication_year":2013,"publication_date":"2013-03-01","ids":{"openalex":"https://openalex.org/W1976645861","doi":"https://doi.org/10.1142/s0218127413500478","mag":"1976645861"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413500478","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500478","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100610292","display_name":"Jihua Wang","orcid":"https://orcid.org/0000-0003-4590-3898"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JIHUA WANG","raw_affiliation_strings":["Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041509169","display_name":"Dongmei Xiao","orcid":"https://orcid.org/0000-0002-6330-578X"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"DONGMEI XIAO","raw_affiliation_strings":["Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030649439","display_name":"Maoan Han","orcid":"https://orcid.org/0000-0001-8792-1256"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"MAOAN HAN","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.345,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78112525,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"23","issue":"03","first_page":"1350047","last_page":"1350047"},"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":1.0,"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":1.0,"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":0.978600025177002,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9462000131607056,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8231918811798096},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6953036785125732},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6526546478271484},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.5946411490440369},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5633760690689087},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5351105332374573},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5003669261932373},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4529380798339844},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44532763957977295},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4267263412475586},{"id":"https://openalex.org/keywords/cusp","display_name":"Cusp (singularity)","score":0.4109098017215729},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16456368565559387}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8231918811798096},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6953036785125732},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6526546478271484},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.5946411490440369},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5633760690689087},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5351105332374573},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5003669261932373},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4529380798339844},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44532763957977295},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4267263412475586},{"id":"https://openalex.org/C2778400075","wikidata":"https://www.wikidata.org/wiki/Q655275","display_name":"Cusp (singularity)","level":2,"score":0.4109098017215729},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16456368565559387},{"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/s0218127413500478","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500478","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W182808185","https://openalex.org/W1531890399","https://openalex.org/W1585821386","https://openalex.org/W1976690062","https://openalex.org/W1979832219","https://openalex.org/W1980247880","https://openalex.org/W1995630721","https://openalex.org/W2004611416","https://openalex.org/W2013677451","https://openalex.org/W2014809428","https://openalex.org/W2019058263","https://openalex.org/W2022102632","https://openalex.org/W2022817035","https://openalex.org/W2022850134","https://openalex.org/W2024729978","https://openalex.org/W2029829738","https://openalex.org/W2031704035","https://openalex.org/W2041988144","https://openalex.org/W2042498362","https://openalex.org/W2052159825","https://openalex.org/W2075420560","https://openalex.org/W2083318543","https://openalex.org/W2087442477","https://openalex.org/W2128949314","https://openalex.org/W3122544035","https://openalex.org/W4294962874"],"related_works":["https://openalex.org/W2587346990","https://openalex.org/W2417802712","https://openalex.org/W2026692681","https://openalex.org/W1965876678","https://openalex.org/W3122961362","https://openalex.org/W3106440911","https://openalex.org/W1631792327","https://openalex.org/W2139245472","https://openalex.org/W2616272482","https://openalex.org/W4231289973"],"abstract_inverted_index":{"In":[0],"this":[1,60,99,124],"paper,":[2],"we":[3,130],"provide":[4],"a":[5,39,48,52,56,139,143,147,151],"complete":[6],"study":[7],"of":[8,11,31,41,59,70,88,90,109,127,135],"the":[9,17,27,32,67,81,86,91,116,132],"zeros":[10,89],"Abelian":[12,94,117,136],"integrals":[13,137],"obtained":[14],"by":[15,47,73],"integrating":[16],"1-form":[18],"(\u03b1":[19],"+":[20,22],"\u03b2x":[21],"x":[23],"2":[24],")ydx":[25],"over":[26],"compact":[28,42],"level":[29,43],"curves":[30,44],"hyperelliptic":[33,61,93],"Hamiltonian":[34,62],"[Formula:":[35],"see":[36],"text].":[37],"Such":[38],"family":[40,69,126],"is":[45,65,78,96],"bounded":[46],"polycycle":[49,140],"passing":[50,141],"through":[51,142],"nilpotent":[53,144],"cusp":[54,145],"and":[55,75,98,146],"hyperbolic":[57,148],"saddle":[58,149],"system,":[63],"which":[64],"not":[66],"exceptional":[68],"ovals":[71],"proposed":[72],"Gavrilov":[74],"Iliev.":[76],"It":[77],"shown":[79],"that":[80,115],"least":[82,100],"upper":[83,101],"bound":[84,102],"for":[85,106,123],"number":[87],"related":[92],"integral":[95,118],"two,":[97],"can":[103],"be":[104],"achieved":[105],"some":[107],"values":[108],"parameters":[110],"(\u03b1,":[111],"\u03b2).":[112],"This":[113],"implies":[114],"still":[119],"has":[120],"Chebyshev":[121],"property":[122],"nonexceptional":[125],"ovals.":[128],"Moreover,":[129],"derive":[131],"asymptotic":[133],"expansion":[134],"near":[138],"in":[150],"general":[152],"case.":[153]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}