{"id":"https://openalex.org/W1985283608","doi":"https://doi.org/10.1137/100807673","title":"Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori","display_name":"Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1985283608","doi":"https://doi.org/10.1137/100807673","mag":"1985283608"},"language":"en","primary_location":{"id":"doi:10.1137/100807673","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100807673","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","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/A5102888195","display_name":"Kenneth R. Meyer","orcid":"https://orcid.org/0000-0001-9778-6983"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kenneth R. Meyer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075274359","display_name":"Jes\u00fas F. Palaci\u00e1n","orcid":"https://orcid.org/0000-0002-0974-6656"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jes\u00fas F. Palaci\u00e1n","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060236004","display_name":"Patricia Yanguas","orcid":"https://orcid.org/0000-0001-9767-5554"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patricia Yanguas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102888195"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1932,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.78455777,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"3","first_page":"817","last_page":"856"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9750999808311462,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9710000157356262,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/kolmogorov\u2013arnold\u2013moser-theorem","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","score":0.7778842449188232},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.7769047021865845},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7045126557350159},{"id":"https://openalex.org/keywords/axial-symmetry","display_name":"Axial symmetry","score":0.6748618483543396},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.6232541799545288},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5420947074890137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5295846462249756},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.44185975193977356},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4288621246814728},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19540944695472717},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.1840517520904541}],"concepts":[{"id":"https://openalex.org/C8522634","wikidata":"https://www.wikidata.org/wiki/Q587081","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","level":3,"score":0.7778842449188232},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.7769047021865845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7045126557350159},{"id":"https://openalex.org/C35377427","wikidata":"https://www.wikidata.org/wiki/Q3886264","display_name":"Axial symmetry","level":2,"score":0.6748618483543396},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6232541799545288},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5420947074890137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5295846462249756},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.44185975193977356},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4288621246814728},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19540944695472717},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1840517520904541},{"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:10.1137/100807673","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100807673","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7799999713897705}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W9659652","https://openalex.org/W122404065","https://openalex.org/W131011303","https://openalex.org/W131775102","https://openalex.org/W133911086","https://openalex.org/W189698414","https://openalex.org/W629298588","https://openalex.org/W1524565983","https://openalex.org/W1541587142","https://openalex.org/W1545683250","https://openalex.org/W1619637304","https://openalex.org/W1620982777","https://openalex.org/W1965927314","https://openalex.org/W1968611432","https://openalex.org/W1970734672","https://openalex.org/W1985080592","https://openalex.org/W1986010423","https://openalex.org/W1987524623","https://openalex.org/W1990419677","https://openalex.org/W1994246733","https://openalex.org/W2002444876","https://openalex.org/W2004602672","https://openalex.org/W2005837982","https://openalex.org/W2010979556","https://openalex.org/W2014510736","https://openalex.org/W2016603813","https://openalex.org/W2020579144","https://openalex.org/W2025115922","https://openalex.org/W2029763489","https://openalex.org/W2031744394","https://openalex.org/W2035078268","https://openalex.org/W2038508018","https://openalex.org/W2044677026","https://openalex.org/W2047062138","https://openalex.org/W2049576205","https://openalex.org/W2054826158","https://openalex.org/W2058206631","https://openalex.org/W2061564692","https://openalex.org/W2068052732","https://openalex.org/W2070402462","https://openalex.org/W2079162259","https://openalex.org/W2082224601","https://openalex.org/W2088035144","https://openalex.org/W2092513812","https://openalex.org/W2113557458","https://openalex.org/W2121511041","https://openalex.org/W2124223428","https://openalex.org/W2124529968","https://openalex.org/W2135739087","https://openalex.org/W2278145264","https://openalex.org/W2531001234","https://openalex.org/W2995963679","https://openalex.org/W3099714760","https://openalex.org/W4237872277","https://openalex.org/W4245545567","https://openalex.org/W4246980133","https://openalex.org/W4251638411","https://openalex.org/W4285719527","https://openalex.org/W4296245916"],"related_works":["https://openalex.org/W1527292232","https://openalex.org/W4232338349","https://openalex.org/W3122252734","https://openalex.org/W4310007495","https://openalex.org/W1968411182","https://openalex.org/W2625596548","https://openalex.org/W2921481273","https://openalex.org/W4385890073","https://openalex.org/W2010444946","https://openalex.org/W25827740"],"abstract_inverted_index":{"We":[0,90,116],"investigate":[1],"the":[2,32,40,55,62,68,76,92,95,103,113,119,125],"dynamics":[3],"of":[4,11,16,58,72,99,107,109,112,121],"various":[5],"problems":[6],"defined":[7],"by":[8,27],"Hamiltonian":[9],"systems":[10,33,63],"two":[12],"and":[13,54,70,97,102,105],"three":[14],"degrees":[15],"freedom":[17],"that":[18,22],"have":[19],"in":[20],"common":[21],"they":[23],"can":[24,44],"be":[25,45],"reduced":[26,65,77],"an":[28,51],"axial":[29],"symmetry.":[30],"Specifically,":[31],"are":[34,64,80],"either":[35],"invariant":[36],"under":[37],"rotation":[38],"about":[39],"vertical":[41],"axis":[42],"or":[43,83],"made":[46],"approximately":[47],"axially":[48],"symmetric":[49],"after":[50],"averaging":[52],"process":[53],"corresponding":[56],"truncation":[57],"higher-order":[59],"terms.":[60],"Once":[61],"we":[66],"study":[67],"existence":[69,96,104,120],"stability":[71,98,106],"relative":[73,100],"equilibria":[74,101],"on":[75],"spaces":[78],"which":[79],"unbounded":[81],"two-":[82],"four-dimensional":[84],"symplectic":[85],"manifolds":[86],"with":[87],"singular":[88],"points.":[89],"establish":[91],"connections":[93],"between":[94],"families":[108],"periodic":[110,126],"solutions":[111],"full":[114],"problem.":[115],"also":[117],"discuss":[118],"KAM":[122],"tori":[123],"surrounding":[124],"solutions.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}