{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T12:11:38Z","timestamp":1761826298819,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2014,11,29]]},"abstract":"<jats:p>We give a short proof of the robustness of the notion of a nonuniform exponential dichotomy for a sequence of linear operators acting on a Banach space. This means that any sufficiently small linear perturbation of a nonuniform exponential dichotomy exhibits the same type of exponential behavior. The method of proof is based on the notion of admissibility introduced by Perron in the special case of a uniform exponential behavior. In strong contrast to former proofs, we do not need to construct explicitly projections on the stable and unstable directions. As an application, we also give a short proof of the robustness of the notion of a nonuniform exponential trichotomy.<\/jats:p>","DOI":"10.4171\/pm\/1953","type":"journal-article","created":{"date-parts":[[2014,11,29]],"date-time":"2014-11-29T17:45:13Z","timestamp":1417283113000},"page":"277-300","source":"Crossref","is-referenced-by-count":4,"title":["Robustness of dichotomies and trichotomies for difference equations"],"prefix":"10.4171","volume":"71","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[{"name":"Instituto Superior T\u00e9cnico, Lisboa, Portugal"}]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico, Lisboa, Portugal"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/PM\/1953","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T12:07:10Z","timestamp":1761826030000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/1953"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,29]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/pm\/1953","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"type":"print","value":"0032-5155"},{"type":"electronic","value":"1662-2758"}],"subject":[],"published":{"date-parts":[[2014,11,29]]}}}