{"id":"https://openalex.org/W2152401606","doi":"https://doi.org/10.1142/s0218127410025405","title":"AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A QUINTIC HAMILTONIAN PLANAR VECTOR FIELD UNDER QUINTIC PERTURBATION","display_name":"AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A QUINTIC HAMILTONIAN PLANAR VECTOR FIELD UNDER QUINTIC PERTURBATION","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2152401606","doi":"https://doi.org/10.1142/s0218127410025405","mag":"2152401606"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127410025405","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410025405","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/A5040950408","display_name":"Tomas Johnson","orcid":"https://orcid.org/0000-0003-4472-5700"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"TOMAS JOHNSON","raw_affiliation_strings":["Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028372442","display_name":"Warwick Tucker","orcid":"https://orcid.org/0000-0001-9888-944X"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"WARWICK TUCKER","raw_affiliation_strings":["Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040950408"],"corresponding_institution_ids":["https://openalex.org/I123387679"],"apc_list":null,"apc_paid":null,"fwci":0.7433,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71414468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"01","first_page":"63","last_page":"70"},"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/T10492","display_name":"Microtubule and mitosis dynamics","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9017000198364258,"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/quintic-function","display_name":"Quintic function","score":0.957982063293457},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6462424397468567},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6379029154777527},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6169004440307617},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6133636236190796},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5942224860191345},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5421775579452515},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5392135381698608},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48948919773101807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46884286403656006},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.4668854773044586},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4517837464809418},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.41144245862960815},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3890901207923889},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.352003812789917},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2097967565059662},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19762903451919556},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18616223335266113},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09954693913459778}],"concepts":[{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.957982063293457},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6462424397468567},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6379029154777527},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6169004440307617},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6133636236190796},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5942224860191345},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5421775579452515},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5392135381698608},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48948919773101807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46884286403656006},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.4668854773044586},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4517837464809418},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.41144245862960815},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3890901207923889},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.352003812789917},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2097967565059662},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19762903451919556},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18616223335266113},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09954693913459778},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127410025405","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410025405","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W82903332","https://openalex.org/W102382135","https://openalex.org/W123447461","https://openalex.org/W190143901","https://openalex.org/W577544449","https://openalex.org/W1483874187","https://openalex.org/W1531890399","https://openalex.org/W1580809199","https://openalex.org/W1968938958","https://openalex.org/W1975987619","https://openalex.org/W1982088565","https://openalex.org/W1992299830","https://openalex.org/W2010073018","https://openalex.org/W2034444332","https://openalex.org/W2049738217","https://openalex.org/W2052155732","https://openalex.org/W2057824738","https://openalex.org/W2060924166","https://openalex.org/W2089876099","https://openalex.org/W2119299479","https://openalex.org/W2124951737","https://openalex.org/W2141310733","https://openalex.org/W2168050314","https://openalex.org/W2196559987","https://openalex.org/W2331620779","https://openalex.org/W2787858293","https://openalex.org/W2792049198","https://openalex.org/W2974264035","https://openalex.org/W3105866591","https://openalex.org/W3144607044","https://openalex.org/W4245729428","https://openalex.org/W4400528399"],"related_works":["https://openalex.org/W4254786939","https://openalex.org/W3148895720","https://openalex.org/W4302555561","https://openalex.org/W4310230578","https://openalex.org/W30258475","https://openalex.org/W2393913406","https://openalex.org/W2329304151","https://openalex.org/W1515531705","https://openalex.org/W3147075732","https://openalex.org/W2949491799"],"abstract_inverted_index":{"The":[0],"limit":[1,33,46],"cycle":[2],"bifurcation":[3],"of":[4,45],"a":[5,52],"Z":[6,15],"2":[7,16],"equivariant":[8,17],"quintic":[9,18,53,58],"planar":[10,54],"Hamiltonian":[11,55],"vector":[12],"field":[13],"under":[14,57],"perturbation":[19],"is":[20,36],"studied.":[21],"We":[22],"prove":[23],"that":[24,48],"the":[25,42],"given":[26],"system":[27,56],"can":[28,49],"have":[29],"at":[30],"least":[31],"27":[32],"cycles.":[34],"This":[35],"an":[37],"improved":[38],"lower":[39],"bound":[40],"on":[41],"possible":[43],"number":[44],"cycles":[47],"bifurcate":[50],"from":[51],"perturbation.":[59]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
