{"id":"https://openalex.org/W2039982162","doi":"https://doi.org/10.1137/110858574","title":"Invariant Manifolds for Analytic Difference Equations","display_name":"Invariant Manifolds for Analytic Difference Equations","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2039982162","doi":"https://doi.org/10.1137/110858574","mag":"2039982162"},"language":"en","primary_location":{"id":"doi:10.1137/110858574","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110858574","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/A5004732229","display_name":"Rafael de la Llave","orcid":"https://orcid.org/0000-0002-0286-6233"},"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":true,"raw_author_name":"Rafael de la Llave","raw_affiliation_strings":["[Georgia Institute of Technology.]"],"affiliations":[{"raw_affiliation_string":"[Georgia Institute of Technology.]","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049444402","display_name":"H\u00e9ctor E. Lomel\u0131\u0301","orcid":null},"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"]},{"id":"https://openalex.org/I187481652","display_name":"Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico","ror":"https://ror.org/029md1766","country_code":"MX","type":"education","lineage":["https://openalex.org/I187481652"]}],"countries":["MX","US"],"is_corresponding":false,"raw_author_name":"H\u00e9ctor E. Lomel\u00ed","raw_affiliation_strings":["\u2021Department of Mathematics Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico Mexico, DF 01000","\u2020School of Mathematics Georgia Institute of Technology Atlanta, GA 30332-0160 USA"],"affiliations":[{"raw_affiliation_string":"\u2021Department of Mathematics Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico Mexico, DF 01000","institution_ids":["https://openalex.org/I187481652"]},{"raw_affiliation_string":"\u2020School of Mathematics Georgia Institute of Technology Atlanta, GA 30332-0160 USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004732229"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.10246462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"4","first_page":"1614","last_page":"1651"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9987999796867371,"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":0.9987999796867371,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9958999752998352,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9833999872207642,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7489565014839172},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6258468627929688},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.6015700101852417},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5929684042930603},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.4949426054954529},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47161439061164856},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.185190349817276},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11557623744010925}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7489565014839172},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6258468627929688},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.6015700101852417},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5929684042930603},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.4949426054954529},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47161439061164856},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.185190349817276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11557623744010925},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110858574","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110858574","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W44921523","https://openalex.org/W123579098","https://openalex.org/W1965429700","https://openalex.org/W1966868006","https://openalex.org/W1989018928","https://openalex.org/W1995249182","https://openalex.org/W2007864255","https://openalex.org/W2014078287","https://openalex.org/W2014386889","https://openalex.org/W2036319645","https://openalex.org/W2045966288","https://openalex.org/W2046424441","https://openalex.org/W2067222304","https://openalex.org/W2082976236","https://openalex.org/W2092099692","https://openalex.org/W2118082066","https://openalex.org/W2127125972","https://openalex.org/W2152106627","https://openalex.org/W2165322512","https://openalex.org/W2315264695","https://openalex.org/W2317594819","https://openalex.org/W2327900111","https://openalex.org/W2328884738","https://openalex.org/W3023854260"],"related_works":["https://openalex.org/W2736737644","https://openalex.org/W3106446297","https://openalex.org/W2385225694","https://openalex.org/W2374325362","https://openalex.org/W2074688623","https://openalex.org/W1913294887","https://openalex.org/W2214763494","https://openalex.org/W2079298033","https://openalex.org/W2354480093","https://openalex.org/W1575974143"],"abstract_inverted_index":{"We":[0,15,127,154],"use":[1],"a":[2,37,84,106,152],"modification":[3],"of":[4,83,148],"the":[5,31,61,76,80,95,99,110,115,122,135,138,145],"parameterization":[6],"method":[7,41],"to":[8,44,131,158],"study":[9,25],"invariant":[10],"manifolds":[11,54,67,70],"for":[12],"difference":[13,32,77,123,161],"equations.":[14,162],"establish":[16],"existence,":[17],"regularity,":[18],"and":[19,24,65,144],"smooth":[20],"dependence":[21],"on":[22],"parameters":[23],"several":[26,132],"singular":[27,120],"limits,":[28],"even":[29],"if":[30,94],"equations":[33,78,82,101],"do":[34],"not":[35,59],"define":[36],"dynamical":[38,107,116],"system.":[39,108],"This":[40],"also":[42,69,155],"leads":[43],"efficient":[45],"algorithms":[46],"that":[47,55],"we":[48,56,88],"present":[49,128,156],"with":[50,72,141,151],"their":[51],"implementations.":[52],"The":[53],"consider":[57],"include":[58],"only":[60],"classical":[62],"strong":[63],"stable":[64],"unstable":[66],"but":[68],"associated":[71],"nonresonant":[73],"spaces.":[74],"When":[75],"are":[79],"Euler--Lagrange":[81,100],"discrete":[85],"variational":[86],"problem,":[87],"have":[89],"sharper":[90],"results.":[91],"Note":[92],"that,":[93],"Legendre":[96,111],"condition":[97,112],"fails,":[98],"cannot":[102],"be":[103,119],"treated":[104],"as":[105],"If":[109],"becomes":[113],"singular,":[114],"system":[117],"may":[118],"while":[121],"equation":[124],"remains":[125],"regular.":[126],"numerical":[129],"applications":[130],"examples":[133],"in":[134],"physics":[136],"literature:":[137],"Frenkel--Kontorova":[139],"model":[140,147],"long-range":[142],"interactions":[143],"Heisenberg":[146],"spin":[149],"chains":[150],"perturbation.":[153],"extensions":[157],"finite":[159],"differentiable":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
