{"id":"https://openalex.org/W1970039091","doi":"https://doi.org/10.1137/12088224x","title":"Rigorous A Posteriori Computation of (Un)Stable Manifolds and Connecting Orbits for Analytic Maps","display_name":"Rigorous A Posteriori Computation of (Un)Stable Manifolds and Connecting Orbits for Analytic Maps","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1970039091","doi":"https://doi.org/10.1137/12088224x","mag":"1970039091"},"language":"en","primary_location":{"id":"doi:10.1137/12088224x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12088224x","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/A5088549920","display_name":"J. D. Mireles James","orcid":"https://orcid.org/0000-0001-8449-9408"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. D. Mireles James","raw_affiliation_strings":["Rutgers, University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rutgers, University","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049298090","display_name":"Konstantin Mischaikow","orcid":"https://orcid.org/0000-0003-2876-4558"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Konstantin Mischaikow","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2467,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.9421403,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"12","issue":"2","first_page":"957","last_page":"1006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9973999857902527,"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":0.9973999857902527,"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":0.9950000047683716,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9842000007629395,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6076924800872803},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5550940036773682},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5048688054084778},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4540676474571228},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.426017701625824},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4201706349849701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3780096471309662},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3338543772697449},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24516567587852478}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6076924800872803},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5550940036773682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5048688054084778},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4540676474571228},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.426017701625824},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4201706349849701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3780096471309662},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3338543772697449},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24516567587852478},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/12088224x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12088224x","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":52,"referenced_works":["https://openalex.org/W44921523","https://openalex.org/W175617483","https://openalex.org/W178772886","https://openalex.org/W201746522","https://openalex.org/W1976107721","https://openalex.org/W1979051148","https://openalex.org/W1989018928","https://openalex.org/W1991658172","https://openalex.org/W1997980245","https://openalex.org/W1998778871","https://openalex.org/W2002361859","https://openalex.org/W2010069926","https://openalex.org/W2010084406","https://openalex.org/W2023892882","https://openalex.org/W2024812061","https://openalex.org/W2025744565","https://openalex.org/W2029331869","https://openalex.org/W2031022267","https://openalex.org/W2035660588","https://openalex.org/W2036319645","https://openalex.org/W2048280869","https://openalex.org/W2049689740","https://openalex.org/W2054589454","https://openalex.org/W2056755069","https://openalex.org/W2058095877","https://openalex.org/W2059226938","https://openalex.org/W2067222304","https://openalex.org/W2068961333","https://openalex.org/W2069902401","https://openalex.org/W2072717148","https://openalex.org/W2076033814","https://openalex.org/W2077011938","https://openalex.org/W2080409870","https://openalex.org/W2080579408","https://openalex.org/W2081657712","https://openalex.org/W2083922917","https://openalex.org/W2089471986","https://openalex.org/W2091233718","https://openalex.org/W2111318856","https://openalex.org/W2124618323","https://openalex.org/W2142065568","https://openalex.org/W2166776051","https://openalex.org/W2170345902","https://openalex.org/W2326026749","https://openalex.org/W2326915604","https://openalex.org/W2335681000","https://openalex.org/W2473089398","https://openalex.org/W2798922842","https://openalex.org/W3038830718","https://openalex.org/W3099526877","https://openalex.org/W3192909774","https://openalex.org/W4213080596"],"related_works":["https://openalex.org/W34626325","https://openalex.org/W2354062721","https://openalex.org/W1576818031","https://openalex.org/W2750854816","https://openalex.org/W4297565432","https://openalex.org/W2951693334","https://openalex.org/W2346542270","https://openalex.org/W2091917844","https://openalex.org/W2170916265","https://openalex.org/W4291306132"],"abstract_inverted_index":{"This":[0],"work":[1],"is":[2,116],"concerned":[3],"with":[4,86],"high":[5],"order":[6,92],"polynomial":[7,27],"approximation":[8],"of":[9,59,69,75,97,106,113,122,128,145],"stable":[10],"and":[11,83,142,151,166],"unstable":[12],"manifolds":[13,82,136],"for":[14,25,100,134,155,160],"analytic":[15,53],"discrete":[16,107],"time":[17,108],"dynamical":[18,109,161],"systems.":[19,110],"We":[20],"develop":[21],"a":[22,41,87,95,147],"posteriori":[23,148],"theorems":[24],"these":[26,76],"approximations":[28],"which":[29,137],"allow":[30],"us":[31],"to":[32,93],"obtain":[33,94,119],"rigorous":[34,84],"bounds":[35,85,150],"on":[36],"the":[37,48,57,60,80,120,123,129,146,152],"truncation":[38,49,61],"errors":[39],"via":[40],"computer":[42],"assisted":[43],"argument.":[44],"Moreover,":[45],"we":[46,78,118],"represent":[47],"error":[50,62,149],"as":[51],"an":[52,73],"function,":[54],"so":[55],"that":[56,117],"derivatives":[58],"can":[63],"be":[64],"bounded":[65],"using":[66],"classical":[67],"estimates":[68],"complex":[70],"analysis.":[71],"As":[72],"application":[74],"ideas":[77],"combine":[79],"approximate":[81],"standard":[88],"Newton--Kantorovich":[89],"argument":[90,154],"in":[91,163],"kind":[96],"\u201canalytic-shadowing\u201d":[98],"result":[99],"connecting":[101,124,156],"orbits":[102,157],"between":[103,140],"fixed":[104],"points":[105],"A":[111],"feature":[112],"this":[114],"method":[115],"transversality":[121],"orbit":[125],"automatically.":[126],"Examples":[127,144],"manifold":[130],"computation":[131],"are":[132,158],"given":[133,159],"invariant":[135],"have":[138],"dimension":[139,164],"two":[141],"ten.":[143],"analytic-shadowing":[153],"systems":[162],"three":[165],"six.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}