{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T03:08:26Z","timestamp":1648868906947},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","funder":[{"name":"FCT\/Portugal","award":["UID\/MAT\/04459\/2013"],"award-info":[{"award-number":["UID\/MAT\/04459\/2013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stoch. Dyn."],"published-print":{"date-parts":[[2018,6]]},"abstract":"<jats:p>We establish the existence of stable invariant manifolds for any sufficiently small perturbation of a cocycle with an exponential dichotomy in mean. The latter notion corresponds to replace the exponential behavior in the classical notion of an exponential dichotomy by an exponential behavior in average with respect to an invariant measure. We consider both perturbations of a cocycle over a map and over a flow that can be defined on an arbitrary Banach space. Moreover, we obtain an upper bound for the speed of the nonlinear dynamics along the stable manifold as well as a lower bound when the exponential dichotomy in mean is strong (this means that we have lower and upper bounds along the stable and unstable directions of the dichotomy).<\/jats:p>","DOI":"10.1142\/s0219493718500223","type":"journal-article","created":{"date-parts":[[2017,5,2]],"date-time":"2017-05-02T04:04:14Z","timestamp":1493697854000},"page":"1850022","source":"Crossref","is-referenced-by-count":1,"title":["Stable manifolds for perturbations of exponential dichotomies in mean"],"prefix":"10.1142","volume":"18","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2018,5,18]]},"reference":[{"key":"S0219493718500223BIB001","doi-asserted-by":"crossref","DOI":"10.1201\/9781420027020","volume-title":"Difference Equations and Inequalities","author":"Agarwal P.","year":"2000"},{"key":"S0219493718500223BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107326026"},{"key":"S0219493718500223BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2005.04.005"},{"key":"S0219493718500223BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2014.08.002"},{"key":"S0219493718500223BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0067780"},{"key":"S0219493718500223BIB006","series-title":"Mathematical Surveys and Monographs","volume-title":"Asymptotic Behavior of Dissipative Systems","volume":"25","author":"Hale J.","year":"1988"},{"key":"S0219493718500223BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089647"},{"key":"S0219493718500223BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5037-9"}],"container-title":["Stochastics and Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219493718500223","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,6]],"date-time":"2020-10-06T17:54:09Z","timestamp":1602006849000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219493718500223"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,18]]},"references-count":8,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2018,5,18]]},"published-print":{"date-parts":[[2018,6]]}},"alternative-id":["10.1142\/S0219493718500223"],"URL":"https:\/\/doi.org\/10.1142\/s0219493718500223","relation":{},"ISSN":["0219-4937","1793-6799"],"issn-type":[{"value":"0219-4937","type":"print"},{"value":"1793-6799","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,18]]}}}