{"id":"https://openalex.org/W2111763954","doi":"https://doi.org/10.1142/s0218127403006662","title":"THE INVARIANT TORI FOR THE 2-MODE DAMPED, DRIVEN SINE-GORDON ODE","display_name":"THE INVARIANT TORI FOR THE 2-MODE DAMPED, DRIVEN SINE-GORDON ODE","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W2111763954","doi":"https://doi.org/10.1142/s0218127403006662","mag":"2111763954"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127403006662","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403006662","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/A5102141701","display_name":"Chi-Jer Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I207776796","display_name":"Overseas Chinese University","ror":"https://ror.org/01j9jq089","country_code":"TW","type":"education","lineage":["https://openalex.org/I207776796"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"CHI-JER YU","raw_affiliation_strings":["Department of Accounting, Overseas Chinese Institute of Technology, Taichung 407, Taiwan, R.O.C"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Accounting, Overseas Chinese Institute of Technology, Taichung 407, Taiwan, R.O.C","institution_ids":["https://openalex.org/I207776796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111901794","display_name":"JONG-EAO LEE","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"JONG-EAO LEE","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan, R.O.C"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan, R.O.C","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20068348,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"02","first_page":"505","last_page":"509"},"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":0.9993000030517578,"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":0.9993000030517578,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.998199999332428,"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/ode","display_name":"Ode","score":0.9288263916969299},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.7908551096916199},{"id":"https://openalex.org/keywords/quasiperiodic-function","display_name":"Quasiperiodic function","score":0.7503684163093567},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.679745078086853},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6206220388412476},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5567104816436768},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5296710729598999},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.43015575408935547},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3262888789176941},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2904762625694275},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.20153746008872986},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18209007382392883},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.135291188955307},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11425390839576721}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.9288263916969299},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.7908551096916199},{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.7503684163093567},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.679745078086853},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6206220388412476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5567104816436768},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5296710729598999},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.43015575408935547},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3262888789176941},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2904762625694275},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.20153746008872986},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18209007382392883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.135291188955307},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11425390839576721},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127403006662","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403006662","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":3,"referenced_works":["https://openalex.org/W1488636064","https://openalex.org/W2097100328","https://openalex.org/W2182274314"],"related_works":["https://openalex.org/W3112195757","https://openalex.org/W2067095166","https://openalex.org/W3206287350","https://openalex.org/W2597882770","https://openalex.org/W4386609754","https://openalex.org/W2800674439","https://openalex.org/W4288753900","https://openalex.org/W2378287236","https://openalex.org/W2799335287","https://openalex.org/W3099151317"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"perform":[4],"our":[5],"algorithm":[6],"developed":[7],"in":[8,26,32],"[Yu":[9],"&amp;":[10],"Lee,":[11],"2001]":[12],"to":[13],"present":[14],"the":[15,23,27,38],"entire":[16],"branches":[17,28],"of":[18,29,35],"quasiperiodic":[19],"solutions":[20,31],"starting":[21],"from":[22],"bifurcation":[24],"points":[25],"periodic":[30],"an":[33],"interval":[34],"parameters":[36],"for":[37],"2-mode":[39],"damped,":[40],"driven":[41],"sine-Gordon":[42],"ODE.":[43]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
