{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:24:07Z","timestamp":1762352647539,"version":"build-2065373602"},"reference-count":34,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,8,12]],"date-time":"2025-08-12T00:00:00Z","timestamp":1754956800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2020-118281GB-C31","PID2021-125535NB-I00","CEX2020-001084-M"],"award-info":[{"award-number":["PID2020-118281GB-C31","PID2021-125535NB-I00","CEX2020-001084-M"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004895","name":"European Social Fund Plus","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004895","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1016\/j.cnsns.2025.109214","type":"journal-article","created":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T01:05:55Z","timestamp":1755824755000},"page":"109214","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"PB","title":["On the convergence of flow map parameterization methods for whiskered tori in quasi-periodic Hamiltonian systems"],"prefix":"10.1016","volume":"152","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3863-0003","authenticated-orcid":false,"given":"\u00c1lvaro","family":"Fern\u00e1ndez-Mora","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c0lex","family":"Haro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Josep-Maria","family":"Mondelo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.cnsns.2025.109214_bib0001","first-page":"527","article-title":"On conservation of conditionally periodic motions for a small change in Hamilton\u2019s function","volume":"98","author":"Kolmogorov","year":"1954","journal-title":"Dokl Akad Nauk SSSR (NS)"},{"issue":"5","key":"10.1016\/j.cnsns.2025.109214_bib0002","first-page":"13","article-title":"Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian","volume":"18","author":"Arnold","year":"1963","journal-title":"Uspehi Mat Nauk"},{"key":"10.1016\/j.cnsns.2025.109214_bib0003","first-page":"1","article-title":"On invariant curves of area-preserving mappings of an annulus","volume":"1962","author":"Moser","year":"1962","journal-title":"Nachr Akad Wiss G\u00f6ttingen Math-Phys Kl II"},{"issue":"2","key":"10.1016\/j.cnsns.2025.109214_bib0004","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1088\/0951-7715\/18\/2\/020","article-title":"KAM theory without action-angle variables","volume":"18","author":"de la Llave","year":"2005","journal-title":"Nonlinearity"},{"issue":"2","key":"10.1016\/j.cnsns.2025.109214_bib0005","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1512\/iumj.2003.52.2245","article-title":"The parameterization method for invariant manifolds. I. Manifolds associated to non-resonant subspaces","volume":"52","author":"Cabr\u00e9","year":"2003","journal-title":"Indiana Univ Math J"},{"issue":"2","key":"10.1016\/j.cnsns.2025.109214_bib0006","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1512\/iumj.2003.52.2407","article-title":"The parameterization method for invariant manifolds. II. Regularity with respect to parameters","volume":"52","author":"Cabr\u00e9","year":"2003","journal-title":"Indiana Univ Math J"},{"issue":"2","key":"10.1016\/j.cnsns.2025.109214_bib0007","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/j.jde.2004.12.003","article-title":"The parameterization method for invariant manifolds. III. Overview and applications","volume":"218","author":"Cabr\u00e9","year":"2005","journal-title":"J Differ Equations"},{"issue":"6","key":"10.1016\/j.cnsns.2025.109214_bib0008","first-page":"1261","article-title":"A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms","volume":"6","author":"Haro","year":"2006","journal-title":"Discrete Contin Dyn Syst Ser-B"},{"issue":"2","key":"10.1016\/j.cnsns.2025.109214_bib0009","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.jde.2005.10.005","article-title":"A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results","volume":"228","author":"Haro","year":"2006","journal-title":"J Differ Equations"},{"issue":"1","key":"10.1016\/j.cnsns.2025.109214_bib0010","doi-asserted-by":"crossref","DOI":"10.1063\/1.2150947","article-title":"Manifolds on the verge of a hyperbolicity breakdown","volume":"16","author":"Haro","year":"2006","journal-title":"Chaos"},{"issue":"8","key":"10.1016\/j.cnsns.2025.109214_bib0011","doi-asserted-by":"crossref","first-page":"3136","DOI":"10.1016\/j.jde.2009.01.037","article-title":"Construction of invariant whiskered tori by a parameterization method. I. Maps and flows in finite dimensions","volume":"246","author":"Fontich","year":"2009","journal-title":"J Differ Equations"},{"issue":"4","key":"10.1016\/j.cnsns.2025.109214_bib0012","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.3934\/dcds.2012.32.1309","article-title":"Computation of whiskered invariant tori and their associated manifolds: new fast algorithms","volume":"32","author":"Huguet","year":"2012","journal-title":"Discrete Contin Dyn Syst"},{"issue":"4","key":"10.1016\/j.cnsns.2025.109214_bib0013","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1088\/0951-7715\/24\/4\/003","article-title":"A KAM theorem without action-angle variables for elliptic lower dimensional tori","volume":"24","author":"Luque","year":"2011","journal-title":"Nonlinearity"},{"issue":"5","key":"10.1016\/j.cnsns.2025.109214_bib0014","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1016\/j.jde.2013.05.001","article-title":"A KAM theory for conformally symplectic systems: efficient algorithms and their validation","volume":"255","author":"Calleja","year":"2013","journal-title":"J Differ Equations"},{"issue":"6","key":"10.1016\/j.cnsns.2025.109214_bib0015","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1007\/s00332-017-9389-y","article-title":"Computation of quasiperiodic normally hyperbolic invariant tori: rigorous results","volume":"27","author":"Canadell","year":"2017","journal-title":"J Nonlinear Sci"},{"key":"10.1016\/j.cnsns.2025.109214_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2021.105859","article-title":"Flow map parameterization methods for invariant tori in hamiltonian systems","volume":"101","author":"Haro","year":"2021","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"3","key":"10.1016\/j.cnsns.2025.109214_bib0017","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1007\/s10208-021-09517-9","article-title":"Efficient and reliable algorithms for the computation of non-twist invariant circles","volume":"22","author":"Gonz\u00e1lez","year":"2022","journal-title":"Found Comput Math"},{"key":"10.1016\/j.cnsns.2025.109214_bib0018","isbn-type":"print","article-title":"The parameterization method for invariant manifolds","volume":"vol. 195","author":"Haro","year":"2016","ISBN":"https:\/\/id.crossref.org\/isbn\/9783319296609"},{"issue":"5","key":"10.1016\/j.cnsns.2025.109214_bib0019","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1007\/s10208-016-9339-3","article-title":"Rigorous computer-assisted application of KAM theory: a modern approach","volume":"17","author":"Figueras","year":"2017","journal-title":"Found Comput Math"},{"key":"10.1016\/j.cnsns.2025.109214_bib0020","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1007\/s00332-016-9342-5","article-title":"A new approach to the parameterization method for Lagrangian tori of Hamiltonian systems","volume":"27","author":"Villanueva","year":"2017","journal-title":"J Nonlinear Sci"},{"key":"10.1016\/j.cnsns.2025.109214_bib0021","doi-asserted-by":"crossref","DOI":"10.1016\/j.physd.2024.134127","article-title":"A modified parameterization method for invariant Lagrangian tori for partially integrable hamiltonian systems","volume":"462","author":"Figueras","year":"2024","journal-title":"Phys D"},{"issue":"4","key":"10.1016\/j.cnsns.2025.109214_bib0022","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/S0167-2789(01)00312-8","article-title":"The dynamics around the collinear equilibrium points of the RTBP","volume":"157","author":"G\u00f3mez","year":"2001","journal-title":"Phys D"},{"issue":"3","key":"10.1016\/j.cnsns.2025.109214_bib0023","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1137\/21M1458363","article-title":"Numerical computation of high-order expansions of invariant manifolds of high-dimensional tori","volume":"21","author":"Gimeno","year":"2022","journal-title":"SIAM J Appl Dyn Syst"},{"issue":"1","key":"10.1016\/j.cnsns.2025.109214_bib0024","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1137\/23M1561257","article-title":"Flow map parameterization methods for invariant tori in quasi-periodic hamiltonian systems","volume":"23","author":"Fern\u00e1ndez-Mora","year":"2024","journal-title":"SIAM J Appl Dyn Syst"},{"key":"10.1016\/j.cnsns.2025.109214_bib0025","series-title":"Dynamical systems, theory and applications (Rencontres, battelle res. inst., seattle, wash., 1974)","first-page":"598","article-title":"On optimal estimates for the solutions of linear partial differential equations of first order with constant coefficients on the torus","author":"R\u00fcssmann","year":"1975"},{"key":"10.1016\/j.cnsns.2025.109214_bib0026","doi-asserted-by":"crossref","unstructured":"Calleja R., Haro \u00c0, Porras P.. \u201cConstructive approaches to QP-time-dependent KAM theory for Lagrangian tori in Hamiltonian systems\u201d. arXiv preprint arXiv:2503.09740(2025).","DOI":"10.1016\/j.jde.2025.113681"},{"key":"10.1016\/j.cnsns.2025.109214_bib0027","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/S1385-7258(68)50059-3","article-title":"Characterization of Anosov diffeomorphisms","volume":"30","author":"Mather","year":"1968","journal-title":"Nederl Akad Wetensch Proc Ser-A 71 = Indag Math"},{"key":"10.1016\/j.cnsns.2025.109214_bib0028","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/0022-0396(74)90067-9","article-title":"Existence of dichotomies and invariant splittings for linear differential systems. I","volume":"15","author":"Sacker","year":"1974","journal-title":"J Differ Equations"},{"issue":"5","key":"10.1016\/j.cnsns.2025.109214_bib0029","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1090\/S0002-9904-1970-12537-X","article-title":"Invariant manifolds","volume":"76","author":"Hirsch","year":"1970","journal-title":"Bull Amer Math Soc"},{"key":"10.1016\/j.cnsns.2025.109214_bib0030","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1090\/S0002-9947-1978-0515539-0","article-title":"Persistent manifolds are normally hyperbolic","volume":"246","author":"Ma\u00f1\u00e9","year":"1978","journal-title":"Trans Amer Math Soc"},{"key":"10.1016\/j.cnsns.2025.109214_bib0031","series-title":"F. casas, v. mart\u00ednez (eds.), advances in differential equations and applications","first-page":"85","article-title":"Parameterization method for computing quasi-periodic reducible normally hyperbolic invariant tori","volume":"vol. 4","author":"Canadell","year":"2014"},{"issue":"6","key":"10.1016\/j.cnsns.2025.109214_bib0032","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1007\/s00332-017-9388-z","article-title":"Computation of quasi-periodic normally hyperbolic invariant tori: algorithms, numerical explorations and mechanisms of breakdown","volume":"27","author":"Canadell","year":"2017","journal-title":"J Nonlinear Sci"},{"key":"10.1016\/j.cnsns.2025.109214_bib0033","first-page":"9","article-title":"Cr-Lohner algorithm","volume":"20","author":"Wilczak","year":"2011","journal-title":"Schedae Inform."},{"key":"10.1016\/j.cnsns.2025.109214_bib0034","article-title":"Efficient usage of self validated integrators for space applications","author":"Alessi","year":"2007","journal-title":"ESA and Universitat de Barcelona TR-07\/5202, Barcelona, Spain"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570425006252?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570425006252?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:13:33Z","timestamp":1762352013000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570425006252"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":34,"alternative-id":["S1007570425006252"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2025.109214","relation":{},"ISSN":["1007-5704"],"issn-type":[{"type":"print","value":"1007-5704"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On the convergence of flow map parameterization methods for whiskered tori in quasi-periodic Hamiltonian systems","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2025.109214","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"109214"}}