{"id":"https://openalex.org/W1990477359","doi":"https://doi.org/10.1137/s0036139900365323","title":"Symmetry and Resonance in Hamiltonian Systems","display_name":"Symmetry and Resonance in Hamiltonian Systems","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1990477359","doi":"https://doi.org/10.1137/s0036139900365323","mag":"1990477359"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139900365323","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139900365323","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://dspace.library.uu.nl:8080/handle/1874/2044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052603280","display_name":"Ferdinand Verhulst","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"F. Verhulst","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023472449","display_name":"Johan Matheus Tuwankotta","orcid":"https://orcid.org/0000-0002-5405-3939"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. M. Tuwankotta","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052603280"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0736,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.76401369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"61","issue":"4","first_page":"1369","last_page":"1385"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13261","display_name":"Elasticity and Wave Propagation","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/resonance","display_name":"Resonance (particle physics)","score":0.7398049831390381},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6196690797805786},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5932636857032776},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5769335627555847},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5675003528594971},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5078151822090149},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.47770336270332336},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4173937141895294},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.37578344345092773},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3601580262184143},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27084168791770935},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10344606637954712}],"concepts":[{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.7398049831390381},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6196690797805786},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5932636857032776},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5769335627555847},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5675003528594971},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5078151822090149},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.47770336270332336},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4173937141895294},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.37578344345092773},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3601580262184143},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27084168791770935},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10344606637954712},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0036139900365323","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139900365323","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dspace.library.uu.nl:1874/2044","is_oa":true,"landing_page_url":"http://dspace.library.uu.nl:8080/handle/1874/2044","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":"","raw_type":"Preprint"},{"id":"pmh:oai:dspace.library.uu.nl:1874/2525","is_oa":true,"landing_page_url":"http://dspace.library.uu.nl:8080/handle/1874/2525","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":"","raw_type":"Preprint"},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/2044","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/2044","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"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":"","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/2525","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/2525","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"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":"","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:dspace.library.uu.nl:1874/2044","is_oa":true,"landing_page_url":"http://dspace.library.uu.nl:8080/handle/1874/2044","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":"","raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8299999833106995,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W58993700","https://openalex.org/W1521160124","https://openalex.org/W1534845734","https://openalex.org/W1550755001","https://openalex.org/W1556059214","https://openalex.org/W1628327903","https://openalex.org/W1965778005","https://openalex.org/W1977849113","https://openalex.org/W1994006347","https://openalex.org/W1994184767","https://openalex.org/W2001413390","https://openalex.org/W2005599022","https://openalex.org/W2020248889","https://openalex.org/W2072599568","https://openalex.org/W2074723508","https://openalex.org/W2077543899","https://openalex.org/W2079764869","https://openalex.org/W2084980020","https://openalex.org/W2126479355","https://openalex.org/W2154161819","https://openalex.org/W2167506368","https://openalex.org/W2212503869","https://openalex.org/W3016105581","https://openalex.org/W3022938717","https://openalex.org/W3047559360","https://openalex.org/W4205471545","https://openalex.org/W4292874936"],"related_works":["https://openalex.org/W2043930649","https://openalex.org/W2912861378","https://openalex.org/W3165633013","https://openalex.org/W2004033414","https://openalex.org/W2044381081","https://openalex.org/W2124353705","https://openalex.org/W83763115","https://openalex.org/W2032214960","https://openalex.org/W2044159598","https://openalex.org/W2129984886"],"abstract_inverted_index":{"In":[0],"this":[1,52],"paper":[2],"we":[3,29,50],"study":[4,78],"resonances":[5,35,98],"in":[6,57],"two":[7],"degrees":[8,26],"of":[9,18,24,27,33,46,55,74,82,97],"freedom,":[10,28],"autonomous,":[11],"Hamiltonian":[12],"systems.":[13],"Due":[14],"to":[15,93],"the":[16,25,34,47,71,88,100,103,107,113],"presence":[17],"a":[19,43,58,79,83,94],"symmetry":[20,65],"condition":[21],"on":[22],"one":[23],"show":[30],"that":[31],"some":[32],"vanish":[36],"as":[37,68,102],"lower":[38],"order":[39,53],"resonances.":[40],"After":[41],"giving":[42],"sharp":[44],"estimate":[45],"resonance":[48,56],"domain,":[49],"investigate":[51],"change":[54],"rather":[59],"general":[60],"potential":[61],"problem":[62],"with":[63,86,99],"discrete":[64],"and":[66,109],"consider":[67],"an":[69],"example":[70,81],"H\u00e9non--Heiles":[72],"family":[73],"Hamiltonians.":[75],"We":[76],"also":[77],"classical":[80],"mechanical":[84],"system":[85],"symmetry,":[87],"elastic":[89],"pendulum,":[90],"which":[91,110],"leads":[92],"natural":[95],"hierarchy":[96],"4:1-resonance":[101],"most":[104],"prominent":[105],"after":[106],"2:1-resonance":[108],"explains":[111],"why":[112],"3:1-resonance":[114],"is":[115],"neglected.":[116]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
