{"id":"https://openalex.org/W2227877641","doi":"https://doi.org/10.1007/s10208-016-9339-3","title":"Rigorous Computer-Assisted Application of KAM Theory: A Modern Approach","display_name":"Rigorous Computer-Assisted Application of KAM Theory: A Modern Approach","publication_year":2016,"publication_date":"2016-11-17","ids":{"openalex":"https://openalex.org/W2227877641","doi":"https://doi.org/10.1007/s10208-016-9339-3","mag":"2227877641"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-016-9339-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-016-9339-3","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.00084","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029803197","display_name":"Jordi-Llu\u00eds Figueras","orcid":"https://orcid.org/0000-0002-0535-4137"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"J.-Ll. Figueras","raw_affiliation_strings":["Departament of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden","Uppsala University"],"affiliations":[{"raw_affiliation_string":"Departament of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]},{"raw_affiliation_string":"Uppsala University","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052725846","display_name":"\u00c0lex Haro","orcid":"https://orcid.org/0000-0003-0377-8099"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Haro","raw_affiliation_strings":["Departament de Matem\u00e0tica Aplicada i An\u00e0lisi, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain","University of Barcelona"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada i An\u00e0lisi, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]},{"raw_affiliation_string":"University of Barcelona","institution_ids":["https://openalex.org/I71999127"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033432509","display_name":"Alejandro Luque","orcid":"https://orcid.org/0000-0002-7813-5656"},"institutions":[{"id":"https://openalex.org/I134820265","display_name":"Consejo Superior de Investigaciones Cient\u00edficas","ror":"https://ror.org/02gfc7t72","country_code":"ES","type":"funder","lineage":["https://openalex.org/I134820265"]},{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Luque","raw_affiliation_strings":["Instituto de Ciencias Matem\u00e1ticas Consejo Superior de Investigaciones Cient\u00edficas, C/ Nicol\u00e1s Cabrera 13-15, 28049, Madrid, Spain","Instituto de Ciencias Matem\u00e1ticas Consejo Superior de Investigaciones Cient\u00edficas Madrid Spain"],"affiliations":[{"raw_affiliation_string":"Instituto de Ciencias Matem\u00e1ticas Consejo Superior de Investigaciones Cient\u00edficas, C/ Nicol\u00e1s Cabrera 13-15, 28049, Madrid, Spain","institution_ids":["https://openalex.org/I4210157032","https://openalex.org/I134820265"]},{"raw_affiliation_string":"Instituto de Ciencias Matem\u00e1ticas Consejo Superior de Investigaciones Cient\u00edficas Madrid Spain","institution_ids":["https://openalex.org/I4210157032","https://openalex.org/I134820265"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029803197"],"corresponding_institution_ids":["https://openalex.org/I123387679"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.2253,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55642736,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"17","issue":"5","first_page":"1123","last_page":"1193"},"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9812999963760376,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9606000185012817,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/standard-map","display_name":"Standard map","score":0.8906640410423279},{"id":"https://openalex.org/keywords/kolmogorov\u2013arnold\u2013moser-theorem","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","score":0.8550723195075989},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7021186947822571},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6999498605728149},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.6803217530250549},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.6585572957992554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6026899814605713},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45935583114624023},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.42221730947494507},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.41747695207595825},{"id":"https://openalex.org/keywords/diophantine-approximation","display_name":"Diophantine approximation","score":0.41274234652519226},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2974414825439453},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2899955213069916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20770564675331116},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09419593214988708},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09179198741912842}],"concepts":[{"id":"https://openalex.org/C82229145","wikidata":"https://www.wikidata.org/wiki/Q2257676","display_name":"Standard map","level":3,"score":0.8906640410423279},{"id":"https://openalex.org/C8522634","wikidata":"https://www.wikidata.org/wiki/Q587081","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","level":3,"score":0.8550723195075989},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7021186947822571},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6999498605728149},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6803217530250549},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.6585572957992554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6026899814605713},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45935583114624023},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.42221730947494507},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.41747695207595825},{"id":"https://openalex.org/C102966492","wikidata":"https://www.wikidata.org/wiki/Q1227061","display_name":"Diophantine approximation","level":3,"score":0.41274234652519226},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2974414825439453},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2899955213069916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20770564675331116},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09419593214988708},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09179198741912842},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10208-016-9339-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-016-9339-3","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1601.00084","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.00084","pdf_url":"https://arxiv.org/pdf/1601.00084","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:diposit.ub.edu:2445/192693","is_oa":false,"landing_page_url":"http://hdl.handle.net/2445/192693","pdf_url":null,"source":{"id":"https://openalex.org/S4306401653","display_name":"Dip\u00f2sit Digital de la Universitat de Barcelona (Universitat de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71999127","host_organization_name":"Universitat de Barcelona","host_organization_lineage":["https://openalex.org/I71999127"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Articles publicats en revistes (Matem\u00e0tiques i Inform\u00e0tica)","raw_type":"info:eu-repo/semantics/acceptedVersion"},{"id":"doi:10.48550/arxiv.1601.00084","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1601.00084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2227877641","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.00084","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.00084","pdf_url":"https://arxiv.org/pdf/1601.00084","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":82,"referenced_works":["https://openalex.org/W28390255","https://openalex.org/W78381459","https://openalex.org/W1480617086","https://openalex.org/W1500147106","https://openalex.org/W1518339998","https://openalex.org/W1535054733","https://openalex.org/W1554728233","https://openalex.org/W1585304689","https://openalex.org/W1594526892","https://openalex.org/W1618237215","https://openalex.org/W1658385597","https://openalex.org/W1659135422","https://openalex.org/W1695477354","https://openalex.org/W1757182457","https://openalex.org/W1868276709","https://openalex.org/W1883076474","https://openalex.org/W1982087766","https://openalex.org/W1984705965","https://openalex.org/W1985764914","https://openalex.org/W1989107981","https://openalex.org/W1998126423","https://openalex.org/W2001375278","https://openalex.org/W2006094273","https://openalex.org/W2007407491","https://openalex.org/W2015777851","https://openalex.org/W2019398782","https://openalex.org/W2021356682","https://openalex.org/W2026806341","https://openalex.org/W2026982913","https://openalex.org/W2028429604","https://openalex.org/W2029122232","https://openalex.org/W2034533638","https://openalex.org/W2037819644","https://openalex.org/W2043466275","https://openalex.org/W2051435621","https://openalex.org/W2052105844","https://openalex.org/W2054130483","https://openalex.org/W2058622906","https://openalex.org/W2063897313","https://openalex.org/W2067503369","https://openalex.org/W2068121196","https://openalex.org/W2071253246","https://openalex.org/W2071973294","https://openalex.org/W2073868859","https://openalex.org/W2075336992","https://openalex.org/W2078637094","https://openalex.org/W2091111385","https://openalex.org/W2094103436","https://openalex.org/W2107996047","https://openalex.org/W2111318856","https://openalex.org/W2120059927","https://openalex.org/W2126581811","https://openalex.org/W2127046795","https://openalex.org/W2153573293","https://openalex.org/W2158677685","https://openalex.org/W2160163816","https://openalex.org/W2163570722","https://openalex.org/W2166761858","https://openalex.org/W2166776051","https://openalex.org/W2169375757","https://openalex.org/W2248977116","https://openalex.org/W2295066694","https://openalex.org/W2315087975","https://openalex.org/W2335681000","https://openalex.org/W2338528753","https://openalex.org/W2389184278","https://openalex.org/W2476794938","https://openalex.org/W2504071824","https://openalex.org/W2504919479","https://openalex.org/W2509243266","https://openalex.org/W2538666553","https://openalex.org/W2593912727","https://openalex.org/W2963039554","https://openalex.org/W2963881724","https://openalex.org/W2964346256","https://openalex.org/W2993547202","https://openalex.org/W3023854260","https://openalex.org/W4230957669","https://openalex.org/W4239194234","https://openalex.org/W4245651583","https://openalex.org/W4247344744","https://openalex.org/W4254470225"],"related_works":["https://openalex.org/W2963867109","https://openalex.org/W2491442521","https://openalex.org/W1970039091","https://openalex.org/W2294573990","https://openalex.org/W2331221349","https://openalex.org/W3046001584","https://openalex.org/W3119512065","https://openalex.org/W3157282745","https://openalex.org/W2037575283","https://openalex.org/W2103696073","https://openalex.org/W1597889683","https://openalex.org/W2963222999","https://openalex.org/W3163612619","https://openalex.org/W2029359030","https://openalex.org/W3106954971","https://openalex.org/W3081814969","https://openalex.org/W3000897791","https://openalex.org/W3197536648","https://openalex.org/W3117984933","https://openalex.org/W3176109468"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
