{"id":"https://openalex.org/W2516244933","doi":"https://doi.org/10.1007/s10208-016-9325-9","title":"Fourier\u2013Taylor Approximation of Unstable Manifolds for Compact Maps: Numerical Implementation and Computer-Assisted Error Bounds","display_name":"Fourier\u2013Taylor Approximation of Unstable Manifolds for Compact Maps: Numerical Implementation and Computer-Assisted Error Bounds","publication_year":2016,"publication_date":"2016-08-25","ids":{"openalex":"https://openalex.org/W2516244933","doi":"https://doi.org/10.1007/s10208-016-9325-9","mag":"2516244933"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-016-9325-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-016-9325-9","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":"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/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. D. Mireles James","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA","institution_ids":["https://openalex.org/I63772739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088549920"],"corresponding_institution_ids":["https://openalex.org/I63772739"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.5465,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84077596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"6","first_page":"1467","last_page":"1523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9896000027656555,"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":0.9896000027656555,"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":0.9822999835014343,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9771999716758728,"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/mathematics","display_name":"Mathematics","score":0.726023256778717},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.627661943435669},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.5435298681259155},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5274729132652283},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5123637914657593},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.490368127822876},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.48374152183532715},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.47039684653282166},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4696749150753021},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4672562777996063},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.45701128244400024},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.44374164938926697},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4328194260597229},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4259136915206909},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3296074867248535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27823883295059204},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16119268536567688}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.726023256778717},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.627661943435669},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5435298681259155},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5274729132652283},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5123637914657593},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.490368127822876},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.48374152183532715},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.47039684653282166},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4696749150753021},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4672562777996063},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.45701128244400024},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.44374164938926697},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4328194260597229},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4259136915206909},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3296074867248535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27823883295059204},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16119268536567688},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-016-9325-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-016-9325-9","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":96,"referenced_works":["https://openalex.org/W44921523","https://openalex.org/W178772886","https://openalex.org/W246508170","https://openalex.org/W603547344","https://openalex.org/W1575147392","https://openalex.org/W1658385597","https://openalex.org/W1695477354","https://openalex.org/W1783410337","https://openalex.org/W1906421350","https://openalex.org/W1965378656","https://openalex.org/W1967216996","https://openalex.org/W1968313583","https://openalex.org/W1970039091","https://openalex.org/W1970608193","https://openalex.org/W1974005577","https://openalex.org/W1974358346","https://openalex.org/W1976876624","https://openalex.org/W1978475451","https://openalex.org/W1979499447","https://openalex.org/W1981833819","https://openalex.org/W1985201401","https://openalex.org/W1988041861","https://openalex.org/W1989018928","https://openalex.org/W1992312556","https://openalex.org/W1993041970","https://openalex.org/W1993430945","https://openalex.org/W1994266397","https://openalex.org/W1994876152","https://openalex.org/W1995676005","https://openalex.org/W1996186996","https://openalex.org/W1998126423","https://openalex.org/W2002361859","https://openalex.org/W2005353159","https://openalex.org/W2010084406","https://openalex.org/W2010626922","https://openalex.org/W2011353941","https://openalex.org/W2018008514","https://openalex.org/W2021708781","https://openalex.org/W2023794945","https://openalex.org/W2023892882","https://openalex.org/W2024812061","https://openalex.org/W2026806341","https://openalex.org/W2029331869","https://openalex.org/W2031022267","https://openalex.org/W2034752323","https://openalex.org/W2036319645","https://openalex.org/W2037575283","https://openalex.org/W2039982162","https://openalex.org/W2041811673","https://openalex.org/W2042795808","https://openalex.org/W2045720672","https://openalex.org/W2050992837","https://openalex.org/W2054589454","https://openalex.org/W2056755069","https://openalex.org/W2059226938","https://openalex.org/W2067222304","https://openalex.org/W2069902401","https://openalex.org/W2071973294","https://openalex.org/W2076033814","https://openalex.org/W2077011938","https://openalex.org/W2080409870","https://openalex.org/W2082578307","https://openalex.org/W2082786393","https://openalex.org/W2090549233","https://openalex.org/W2093569281","https://openalex.org/W2097894461","https://openalex.org/W2104795820","https://openalex.org/W2118884582","https://openalex.org/W2124529968","https://openalex.org/W2138744670","https://openalex.org/W2154742871","https://openalex.org/W2162228740","https://openalex.org/W2166776051","https://openalex.org/W2169375757","https://openalex.org/W2170345902","https://openalex.org/W2170449240","https://openalex.org/W2278746223","https://openalex.org/W2323454677","https://openalex.org/W2323571385","https://openalex.org/W2326026749","https://openalex.org/W2335681000","https://openalex.org/W2342188647","https://openalex.org/W2389184278","https://openalex.org/W2472758162","https://openalex.org/W2535934392","https://openalex.org/W2607287562","https://openalex.org/W2963074510","https://openalex.org/W2963881724","https://openalex.org/W2963924144","https://openalex.org/W2964338477","https://openalex.org/W2994713664","https://openalex.org/W3098005432","https://openalex.org/W3104736809","https://openalex.org/W3105187499","https://openalex.org/W3182252275","https://openalex.org/W4254470225"],"related_works":["https://openalex.org/W2040666836","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W1990789772","https://openalex.org/W138907054","https://openalex.org/W2073959938","https://openalex.org/W2536422707","https://openalex.org/W24145419","https://openalex.org/W2036329708"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}