{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T20:17:53Z","timestamp":1648844273398},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2013,6,28]],"date-time":"2013-06-28T00:00:00Z","timestamp":1372377600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Edinburgh Mathematical Society"],"published-print":{"date-parts":[[2013,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a sequence of matrices<jats:italic>(A<jats:sub>m<\/jats:sub>)<\/jats:italic><jats:sub><jats:italic>m<\/jats:italic>\u2208\u2115<\/jats:sub>whose Lyapunov exponents are limits, we show that this asymptotic behaviour is reproduced by the sequences<jats:italic>x<\/jats:italic><jats:sub><jats:italic>m<\/jats:italic>+1<\/jats:sub>=<jats:italic>A<jats:sub>m<\/jats:sub>x<jats:sub>m<\/jats:sub>+ f<jats:sub>m<\/jats:sub>(x<jats:sub>m<\/jats:sub>)<\/jats:italic>for any sufficiently small perturbations<jats:italic>f<jats:sub>m<\/jats:sub><\/jats:italic>. We also consider the general case of exponential rates e<jats:sup><jats:italic>c\u03c1<jats:sub>m<\/jats:sub><\/jats:italic><\/jats:sup>for an arbitrary increasing sequence<jats:italic>\u03c1<jats:sub>m<\/jats:sub><\/jats:italic>. Our approach is based on Lyapunov's theory of regularity.<\/jats:p>","DOI":"10.1017\/s0013091513000382","type":"journal-article","created":{"date-parts":[[2013,8,19]],"date-time":"2013-08-19T08:08:08Z","timestamp":1376899688000},"page":"643-656","source":"Crossref","is-referenced-by-count":0,"title":["On the exponential behaviour of non-autonomous difference equations"],"prefix":"10.1017","volume":"56","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2013,6,28]]},"reference":[{"key":"S0013091513000382_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.04.027"},{"key":"S0013091513000382_ref006","volume-title":"Heath Mathematical Monographs","author":"Coppel","year":"1965"},{"key":"S0013091513000382_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01180524"},{"key":"S0013091513000382_ref003","volume-title":"Lecture Notes in Mathematics","volume":"1926","author":"Barreira","year":"2008"},{"key":"S0013091513000382_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1964-0156122-9"},{"key":"S0013091513000382_ref001","volume-title":"University Lecture Series","volume":"23","author":"Barreira","year":"2002"},{"key":"S0013091513000382_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2007.10.017"},{"key":"S0013091513000382_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/2372422"},{"key":"S0013091513000382_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.09.081"},{"key":"S0013091513000382_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulsci.2011.12.003"},{"key":"S0013091513000382_ref002","volume-title":"Encyclopedia of Mathematics and Its Applications","volume":"115","author":"Barreira","year":"2007"},{"key":"S0013091513000382_ref008","doi-asserted-by":"crossref","unstructured":"Lettenmeyer F. , \u00dcber das asymptotische Verhalten der L\u00f6sungen von Differentialgleichungen und Differentialgleichungssystemen (Verlag der Bayerische Akademie der Wissenschaften, M\u00fcnchen, 1929).","DOI":"10.1515\/9783486763522"}],"container-title":["Proceedings of the Edinburgh Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0013091513000382","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,2]],"date-time":"2020-08-02T04:50:51Z","timestamp":1596343851000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0013091513000382\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,28]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,10]]}},"alternative-id":["S0013091513000382"],"URL":"https:\/\/doi.org\/10.1017\/s0013091513000382","relation":{},"ISSN":["0013-0915","1464-3839"],"issn-type":[{"value":"0013-0915","type":"print"},{"value":"1464-3839","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6,28]]}}}