{"id":"https://openalex.org/W2066498158","doi":"https://doi.org/10.1142/s0218127405013678","title":"NINETY PLUS THIRTY YEARS OF NONLINEAR DYNAMICS: LESS IS MORE AND MORE IS DIFFERENT","display_name":"NINETY PLUS THIRTY YEARS OF NONLINEAR DYNAMICS: LESS IS MORE AND MORE IS DIFFERENT","publication_year":2005,"publication_date":"2005-09-01","ids":{"openalex":"https://openalex.org/W2066498158","doi":"https://doi.org/10.1142/s0218127405013678","mag":"2066498158"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405013678","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013678","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/A5053868357","display_name":"Philip Holmes","orcid":"https://orcid.org/0000-0002-1459-7157"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"PHILIP HOLMES","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA","Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053868357"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":2.4622,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.90541469,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"09","first_page":"2703","last_page":"2716"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9879000186920166,"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/T10044","display_name":"Protein Structure and Dynamics","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular 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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6970648765563965},{"id":"https://openalex.org/keywords/mathematical-and-theoretical-biology","display_name":"Mathematical and theoretical biology","score":0.6177957057952881},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5729146003723145},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47920069098472595},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4714285731315613},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46836578845977783},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.46749556064605713},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4590967297554016},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4408488869667053},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.41203564405441284},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.403882771730423},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.37491855025291443},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3630225956439972},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24535351991653442},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22414517402648926},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.12230506539344788},{"id":"https://openalex.org/keywords/bioinformatics","display_name":"Bioinformatics","score":0.0884748101234436},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07113876938819885},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06891703605651855}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6970648765563965},{"id":"https://openalex.org/C20129857","wikidata":"https://www.wikidata.org/wiki/Q751611","display_name":"Mathematical and theoretical biology","level":2,"score":0.6177957057952881},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5729146003723145},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47920069098472595},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4714285731315613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46836578845977783},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.46749556064605713},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4590967297554016},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4408488869667053},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.41203564405441284},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.403882771730423},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.37491855025291443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3630225956439972},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24535351991653442},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22414517402648926},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.12230506539344788},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0884748101234436},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07113876938819885},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06891703605651855},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127405013678","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013678","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.597.7557","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.597.7557","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.princeton.edu/mae/people/faculty/holmes/Publishings/ninety plus thirty years.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":125,"referenced_works":["https://openalex.org/W15911136","https://openalex.org/W47140119","https://openalex.org/W72552736","https://openalex.org/W99189181","https://openalex.org/W126935648","https://openalex.org/W201746522","https://openalex.org/W202712393","https://openalex.org/W572135912","https://openalex.org/W626804930","https://openalex.org/W1427593441","https://openalex.org/W1486029386","https://openalex.org/W1496798092","https://openalex.org/W1533733939","https://openalex.org/W1546156674","https://openalex.org/W1546721432","https://openalex.org/W1550227333","https://openalex.org/W1558736232","https://openalex.org/W1561704653","https://openalex.org/W1562360371","https://openalex.org/W1567812234","https://openalex.org/W1579236455","https://openalex.org/W1582846995","https://openalex.org/W1591424923","https://openalex.org/W1594759473","https://openalex.org/W1596321532","https://openalex.org/W1633869374","https://openalex.org/W1659716324","https://openalex.org/W1802196594","https://openalex.org/W1876456565","https://openalex.org/W1965778005","https://openalex.org/W1969836308","https://openalex.org/W1970765391","https://openalex.org/W1976213300","https://openalex.org/W1979265581","https://openalex.org/W1981479913","https://openalex.org/W1982587838","https://openalex.org/W1983815930","https://openalex.org/W1983924943","https://openalex.org/W1985940938","https://openalex.org/W1998126423","https://openalex.org/W2001399206","https://openalex.org/W2008962126","https://openalex.org/W2009433941","https://openalex.org/W2027595215","https://openalex.org/W2029716246","https://openalex.org/W2030669316","https://openalex.org/W2030787748","https://openalex.org/W2032192133","https://openalex.org/W2035695789","https://openalex.org/W2052683749","https://openalex.org/W2056529601","https://openalex.org/W2058897724","https://openalex.org/W2059625173","https://openalex.org/W2061301711","https://openalex.org/W2062427814","https://openalex.org/W2071290058","https://openalex.org/W2080187730","https://openalex.org/W2081817659","https://openalex.org/W2083115202","https://openalex.org/W2083633830","https://openalex.org/W2085742756","https://openalex.org/W2089876099","https://openalex.org/W2090359786","https://openalex.org/W2090814006","https://openalex.org/W2093937828","https://openalex.org/W2094008907","https://openalex.org/W2101075974","https://openalex.org/W2101714536","https://openalex.org/W2103285029","https://openalex.org/W2112348994","https://openalex.org/W2112602754","https://openalex.org/W2114385471","https://openalex.org/W2128949314","https://openalex.org/W2139168617","https://openalex.org/W2141394518","https://openalex.org/W2142933474","https://openalex.org/W2143980865","https://openalex.org/W2149525340","https://openalex.org/W2164260548","https://openalex.org/W2169896642","https://openalex.org/W2170105115","https://openalex.org/W2223026876","https://openalex.org/W2315938601","https://openalex.org/W2316463358","https://openalex.org/W2318340538","https://openalex.org/W2328151902","https://openalex.org/W2480701976","https://openalex.org/W2486576829","https://openalex.org/W2489347996","https://openalex.org/W2495772062","https://openalex.org/W2500278320","https://openalex.org/W2611584071","https://openalex.org/W2797781694","https://openalex.org/W3013347551","https://openalex.org/W3025560754","https://openalex.org/W3107714133","https://openalex.org/W3123094903","https://openalex.org/W3138705879","https://openalex.org/W3149545211","https://openalex.org/W4205579805","https://openalex.org/W4205727720","https://openalex.org/W4211016790","https://openalex.org/W4212928962","https://openalex.org/W4212958445","https://openalex.org/W4213213245","https://openalex.org/W4213264637","https://openalex.org/W4230971143","https://openalex.org/W4233958670","https://openalex.org/W4234284487","https://openalex.org/W4234436290","https://openalex.org/W4234555707","https://openalex.org/W4240399370","https://openalex.org/W4241846002","https://openalex.org/W4245364320","https://openalex.org/W4245511121","https://openalex.org/W4245643085","https://openalex.org/W4252439913","https://openalex.org/W4252911570","https://openalex.org/W4253294199","https://openalex.org/W4292366057","https://openalex.org/W4293079168","https://openalex.org/W4294553796","https://openalex.org/W4294967943","https://openalex.org/W4298860934","https://openalex.org/W4301656904"],"related_works":["https://openalex.org/W2353039109","https://openalex.org/W2900100504","https://openalex.org/W4315588385","https://openalex.org/W3124638673","https://openalex.org/W2066153363","https://openalex.org/W2061564118","https://openalex.org/W4318566977","https://openalex.org/W4254898719","https://openalex.org/W2146196898","https://openalex.org/W42028307"],"abstract_inverted_index":{"I":[0,31,52],"review":[1],"the":[2,77],"early":[3],"(1885\u20131975)":[4],"and":[5,16,26,38,43,67,79],"more":[6],"recent":[7,36],"history":[8],"of":[9,20,28],"dynamical":[10],"systems":[11],"theory,":[12],"identifying":[13],"key":[14],"principles":[15],"themes,":[17],"including":[18],"those":[19],"dimension":[21],"reduction,":[22],"normal":[23],"form":[24],"transformation":[25],"unfolding":[27],"degenerate":[29],"cases.":[30],"end":[32],"by":[33,63],"briefly":[34],"noting":[35],"extensions":[37],"applications":[39],"in":[40],"nonlinear":[41,64],"fluid":[42],"solid":[44],"mechanics,":[45],"with":[46],"a":[47,70],"nod":[48],"toward":[49],"mathematical":[50,58],"biology.":[51],"argue":[53],"throughout":[54,76],"that":[55,68],"this":[56],"essentially":[57],"theory":[59],"was":[60],"largely":[61],"motivated":[62],"scientific":[65],"problems,":[66],"after":[69],"long":[71],"gestation":[72],"it":[73],"is":[74],"propagating":[75],"sciences":[78],"technology.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}