{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T16:57:45Z","timestamp":1649091465707},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Anal. Appl."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p> We establish the existence of stable manifolds under sufficiently small perturbations of a linear impulsive equation. Our results are optimal, in the sense that for vector fields of class C<jats:sup>1<\/jats:sup> outside the jumping times, the invariant manifolds are also of class C<jats:sup>1<\/jats:sup> outside these times. We also consider the case of C<jats:sup>1<\/jats:sup> parameter-dependent perturbations and we establish the C<jats:sup>1<\/jats:sup> dependence of the stable manifolds on the parameter. The proof uses the fiber contraction principle. We emphasize that we consider the general case of nonautonomous equations for which the linear part has a nonuniform exponential dichotomy. <\/jats:p>","DOI":"10.1142\/s0219530514500092","type":"journal-article","created":{"date-parts":[[2013,12,14]],"date-time":"2013-12-14T07:47:45Z","timestamp":1387007265000},"page":"131-160","source":"Crossref","is-referenced-by-count":0,"title":["PARAMETER DEPENDENCE OF STABLE MANIFOLDS FOR IMPULSIVE EQUATIONS"],"prefix":"10.1142","volume":"12","author":[{"given":"LUIS","family":"BARREIRA","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, 1049-001 Lisboa, Portugal"}]},{"given":"CLAUDIA","family":"VALLS","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, 1049-001 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2014,2,27]]},"reference":[{"key":"rf1","series-title":"University Lecture Series","volume-title":"Lyapunov Exponents and Smooth Ergodic Theory","volume":"23","author":"Barreira L.","year":"2002"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107326026"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74775-8"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-010-9161-6"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/0906"},{"key":"rf6","first-page":"197","volume":"19","author":"Oseledets V.","journal-title":"Trans. Moscow Math. Soc."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1070\/IM1976v010n06ABEH001835"},{"key":"rf8","series-title":"Nonlinear Science Series A: Monographs and Treatises","doi-asserted-by":"crossref","DOI":"10.1142\/2892","volume-title":"Impulsive Differential Equations","volume":"14","author":"Samoilenko A.","year":"1995"}],"container-title":["Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219530514500092","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:09:20Z","timestamp":1565118560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219530514500092"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,27]]},"references-count":8,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,2,27]]},"published-print":{"date-parts":[[2014,3]]}},"alternative-id":["10.1142\/S0219530514500092"],"URL":"https:\/\/doi.org\/10.1142\/s0219530514500092","relation":{},"ISSN":["0219-5305","1793-6861"],"issn-type":[{"value":"0219-5305","type":"print"},{"value":"1793-6861","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2,27]]}}}