{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T19:37:09Z","timestamp":1764963429570,"version":"3.46.0"},"reference-count":5,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010,2,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this note we consider the notion of nonuniform exponential contraction for delay difference equations with infinite delay (one can argue that the only delay difference equations are those with infinite delay, since otherwise we can always bring them to the standard recurrence form in some higher-dimensional space). We consider the general case of a nonautonomous dynamics. Our main objective is to show that exponential contractions persist under sufficiently small linear and nonlinear perturbations. This includes establishing the continuous dependence with the perturbation of the constants in the notion of contraction. We also characterize the nonuniform exponential contractions in terms of strict Lyapunov sequences, in particular by constructing explicitly a strict Lyapunov sequence for each exponential contraction.<\/jats:p>","DOI":"10.1515\/ans-2010-0106","type":"journal-article","created":{"date-parts":[[2016,3,11]],"date-time":"2016-03-11T06:42:54Z","timestamp":1457678574000},"page":"121-129","source":"Crossref","is-referenced-by-count":0,"title":["Nonuniform Stability of Difference Equations with Infinite Delay"],"prefix":"10.1515","volume":"10","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":"374","published-online":{"date-parts":[[2016,3,10]]},"reference":[{"key":"ref11","first-page":"238","article-title":"Stability in delay difference equations with nonuniform expo - nential behavior Differential","author":"Barreira","year":"2007","journal-title":"Equations"},{"key":"ref01","first-page":"23","article-title":"Exponents and Smooth Ergodic Theory sity Lecture Series","author":"Barreira","year":"2002","journal-title":"Lyapunov Math Soc"},{"key":"ref21","first-page":"244","article-title":"Robustness of nonuniform exponential dichotomies in Banach spaces Differential","author":"Barreira","year":"2008","journal-title":"Equations"},{"key":"ref41","first-page":"629","article-title":"Dichotomies in Stability Theory in","author":"Coppel","year":"1978","journal-title":"Notes Math"},{"key":"ref51","first-page":"51","article-title":"Ma \u0131zel On stability of solutions of systems of differential equations","author":"Ural","year":"1954","journal-title":"Inst"}],"container-title":["Advanced Nonlinear Studies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/ans-2010-0106\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/ans-2010-0106\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T19:13:48Z","timestamp":1764962028000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/ans-2010-0106\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,1]]},"references-count":5,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3,10]]},"published-print":{"date-parts":[[2010,2,1]]}},"alternative-id":["10.1515\/ans-2010-0106"],"URL":"https:\/\/doi.org\/10.1515\/ans-2010-0106","relation":{},"ISSN":["2169-0375","1536-1365"],"issn-type":[{"type":"electronic","value":"2169-0375"},{"type":"print","value":"1536-1365"}],"subject":[],"published":{"date-parts":[[2010,2,1]]}}}