{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T22:23:09Z","timestamp":1773267789936,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Math."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p> For a nonautonomous dynamics defined by a sequence of linear operators, we introduce the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility in l<jats:sup>p<\/jats:sup> spaces, both for the space of perturbations and the space of solutions. This allows unifying the notions of uniform and nonuniform exponential behavior. Moreover, we consider the general case of a noninvertible dynamics. As a nontrivial application we show that the conditional stability of a nonuniform exponential dichotomy persists under sufficiently small linear perturbations. <\/jats:p>","DOI":"10.1142\/s0129167x14500244","type":"journal-article","created":{"date-parts":[[2014,3,4]],"date-time":"2014-03-04T02:39:45Z","timestamp":1393900785000},"page":"1450024","source":"Crossref","is-referenced-by-count":10,"title":["Exponential dichotomies with respect to a sequence of norms and admissibility"],"prefix":"10.1142","volume":"25","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, 1049-001 Lisboa, Portugal"}]},{"given":"Davor","family":"Dragi\u010devi\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Rijeka, 51000 Rijeka, Croatia"}]},{"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":[[2014,4,3]]},"reference":[{"key":"rf2","series-title":"University Lecture Series","volume-title":"Lyapunov Exponents and Smooth Ergodic Theory","volume":"23","author":"Barreira L.","year":"2002"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.02.028"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74775-8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8615-4_3"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01063733"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/070"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1995.1117"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(67)90014-9"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0065310"},{"key":"rf11","series-title":"Translations of Mathematical Monographs","volume-title":"Stability of Solutions of Differential Equations in Banach Space","volume":"43","author":"Dalecki\u012d Ju.","year":"1974"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089647"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2005.11.002"},{"key":"rf14","first-page":"387","volume":"58","author":"Latushkin Yu.","journal-title":"J. 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