{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T06:04:59Z","timestamp":1648965899893},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2016,11,4]],"date-time":"2016-11-04T00:00:00Z","timestamp":1478217600000},"content-version":"unspecified","delay-in-days":217,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[2016,4]]},"abstract":"<jats:p>For a dynamics on the whole line, for both discrete and continuous time, we extend a result of Pliss that gives a characterization of the notion of a trichotomy in various directions. More precisely, the result gives a characterization in terms of an admissibility property in the whole line (namely, the existence of bounded solutions of a linear dynamics under any nonlinear bounded perturbation) of the existence of a trichotomy, i.e. of exponential dichotomies in the future and in the past, together with a certain transversality condition at time zero. In particular, we consider arbitrary linear operators acting on a Banach space as well as sequences of norms instead of a single norm, which allows us to consider the general case of non-uniform exponential behaviour.<\/jats:p>","DOI":"10.1017\/s0308210516000123","type":"journal-article","created":{"date-parts":[[2016,11,4]],"date-time":"2016-11-04T09:04:26Z","timestamp":1478250266000},"page":"225-243","source":"Crossref","is-referenced-by-count":1,"title":["A version of a theorem of Pliss for non-uniform and non-invertible dichotomies"],"prefix":"10.1017","volume":"147","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[]},{"given":"Davor","family":"Dragi\u010devi\u0107","sequence":"additional","affiliation":[]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,11,4]]},"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210516000123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T00:56:40Z","timestamp":1555549000000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210516000123\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,4]]}},"alternative-id":["S0308210516000123"],"URL":"https:\/\/doi.org\/10.1017\/s0308210516000123","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4]]}}}