{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:58:23Z","timestamp":1773147503504,"version":"3.50.1"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Commun. Contemp. Math."],"published-print":{"date-parts":[[2018,6]]},"abstract":"<jats:p> We give a complete characterization of the existence of Lyapunov coordinate changes bringing an invertible sequence of matrices to one in block form. In other words, we give a criterion for the block-trivialization of a nonautonomous dynamics with discrete time while preserving the asymptotic properties of the dynamics. We provide two nontrivial applications of this criterion: we show that any Lyapunov regular sequence of invertible matrices can be transformed by a Lyapunov coordinate change into a constant diagonal sequence; and we show that the family of all coordinate changes preserving simultaneously the Lyapunov exponents of all sequences of invertible matrices (with finite exponent) coincides with the family of Lyapunov coordinate changes. <\/jats:p>","DOI":"10.1142\/s0219199717500274","type":"journal-article","created":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T08:13:08Z","timestamp":1487319188000},"page":"1750027","source":"Crossref","is-referenced-by-count":7,"title":["Transformations preserving the Lyapunov exponents"],"prefix":"10.1142","volume":"20","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2018,5,20]]},"reference":[{"key":"S0219199717500274BIB001","doi-asserted-by":"publisher","DOI":"10.1134\/S0012266107120026"},{"key":"S0219199717500274BIB002","doi-asserted-by":"publisher","DOI":"10.1134\/S0012266112120014"},{"key":"S0219199717500274BIB003","series-title":"University Lecture Series","volume-title":"Lyapunov Exponents and Smooth Ergodic Theory","volume":"23","author":"Barreira L.","year":"2002"},{"key":"S0219199717500274BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107326026"},{"key":"S0219199717500274BIB005","first-page":"1359","volume":"23","author":"Bylov B.","year":"1987","journal-title":"Differ. Equ."},{"key":"S0219199717500274BIB006","volume-title":"Theory of Lyapunov Exponents and Its Application to Problems of Stability","author":"Bylov B.","year":"1966"}],"container-title":["Communications in Contemporary Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219199717500274","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:21:30Z","timestamp":1565126490000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219199717500274"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,20]]},"references-count":6,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2018,5,20]]},"published-print":{"date-parts":[[2018,6]]}},"alternative-id":["10.1142\/S0219199717500274"],"URL":"https:\/\/doi.org\/10.1142\/s0219199717500274","relation":{},"ISSN":["0219-1997","1793-6683"],"issn-type":[{"value":"0219-1997","type":"print"},{"value":"1793-6683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,20]]}}}