{"id":"https://openalex.org/W2033368462","doi":"https://doi.org/10.1103/physrev.188.416","title":"Amplitude Instability and Ergodic Behavior for Conservative Nonlinear Oscillator Systems","display_name":"Amplitude Instability and Ergodic Behavior for Conservative Nonlinear Oscillator Systems","publication_year":1969,"publication_date":"1969-12-05","ids":{"openalex":"https://openalex.org/W2033368462","doi":"https://doi.org/10.1103/physrev.188.416","mag":"2033368462"},"language":"en","primary_location":{"id":"doi:10.1103/physrev.188.416","doi":"https://doi.org/10.1103/physrev.188.416","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrev.188.416","pdf_url":null,"source":{"id":"https://openalex.org/S54862371","display_name":"Physical Review","issn_l":"0031-899X","issn":["0031-899X","1536-6065"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2033368462"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5078333691","display_name":"Grayson H. Walker","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Grayson H. Walker","raw_affiliation_strings":["School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036077461","display_name":"Joseph Ford","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph Ford","raw_affiliation_strings":["School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":5.7349,"has_fulltext":false,"cited_by_count":298,"citation_normalized_percentile":{"value":0.9637883,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"188","issue":"1","first_page":"416","last_page":"432"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.004600000102072954,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.0006000000284984708,"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/amplitude-instability","display_name":"amplitude instability","score":0.9769999980926514},{"id":"https://openalex.org/keywords/ergodic-behavior","display_name":"ergodic behavior","score":0.777999997138977},{"id":"https://openalex.org/keywords/kam-theory","display_name":"KAM theory","score":0.703000009059906},{"id":"https://openalex.org/keywords/onset-of-instability","display_name":"onset of instability","score":0.6650000214576721},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"statistical mechanics","score":0.8029999732971191},{"id":"https://openalex.org/keywords/hamiltonian-systems","display_name":"Hamiltonian systems","score":0.4950000047683716}],"concepts":[{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.8712343573570251},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.7427676916122437},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7320398092269897},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.6575224995613098},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5912572741508484},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5834949612617493},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5280473828315735},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.47048166394233704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37511590123176575},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.30554452538490295},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30521783232688904}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1103/physrev.188.416","doi":"https://doi.org/10.1103/physrev.188.416","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrev.188.416","pdf_url":null,"source":{"id":"https://openalex.org/S54862371","display_name":"Physical Review","issn_l":"0031-899X","issn":["0031-899X","1536-6065"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1970570875","https://openalex.org/W1972481136","https://openalex.org/W1973536581","https://openalex.org/W1979129393","https://openalex.org/W1979310283","https://openalex.org/W1992183637","https://openalex.org/W1994006347","https://openalex.org/W2023456906","https://openalex.org/W2028570329","https://openalex.org/W2034018919","https://openalex.org/W2036113683","https://openalex.org/W2036383724","https://openalex.org/W2058622906","https://openalex.org/W2066459356","https://openalex.org/W2072103899","https://openalex.org/W2073868859","https://openalex.org/W2082893690","https://openalex.org/W2113194592","https://openalex.org/W2115298982","https://openalex.org/W2162829276","https://openalex.org/W2163570722","https://openalex.org/W2326892736","https://openalex.org/W2327820340","https://openalex.org/W2503500554","https://openalex.org/W4242450404","https://openalex.org/W4251030244","https://openalex.org/W4392306314"],"related_works":["https://openalex.org/W2038620460","https://openalex.org/W2041871620","https://openalex.org/W2735236306","https://openalex.org/W7143744093","https://openalex.org/W3088613483","https://openalex.org/W2122237834","https://openalex.org/W3041627413","https://openalex.org/W2135928306","https://openalex.org/W1623810643","https://openalex.org/W4244237906"],"abstract_inverted_index":{"Several":[0],"earlier":[1,116],"computer":[2],"studies":[3],"of":[4,33,45,48,81,125],"nonlinear":[5],"oscillator":[6,98],"systems":[7,99],"have":[8,26],"revealed":[9],"an":[10,64],"amplitude":[11,69,91,126],"instability":[12,70,92,127],"marking":[13],"a":[14,34,74,103],"sharp":[15],"transition":[16],"from":[17],"conditionally":[18],"periodic":[19],"to":[20,38,51,56,62,67,72,102,114,122],"ergodic-type":[21],"motion,":[22],"and":[23,41,71,105],"several":[24,52,115],"authors":[25],"explained":[27],"the":[28,46,79,123],"observed":[29],"instabilities":[30],"in":[31,96],"terms":[32],"mathematical":[35],"theorem":[36],"due":[37],"Kolmogorov,":[39],"Arnol'd,":[40],"Moser.":[42],"In":[43],"view":[44],"significance":[47],"these":[49],"results":[50],"diverse":[53],"fields,":[54],"especially":[55],"statistical":[57,129],"mechanics,":[58],"this":[59,82],"paper":[60],"attempts":[61],"provide":[63,73],"elementary":[65],"introduction":[66],"Kolmogorov-Arnol'd-Moser":[68],"verifiable":[75],"scheme":[76],"for":[77,128],"predicting":[78],"onset":[80],"instability.":[83],"This":[84],"goal":[85],"is":[86,112,120],"achieved":[87],"by":[88],"demonstrating":[89],"that":[90],"can":[93],"occur":[94],"even":[95],"simple":[97],"which":[100],"admit":[101],"clear":[104],"detailed":[106],"analysis.":[107],"The":[108],"analysis":[109],"presented":[110],"here":[111],"related":[113],"studies.":[117],"Special":[118],"attention":[119],"given":[121],"relevance":[124],"mechanics.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
