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This concept of local approximation is applied to the study of local uniform asymptotic stability, leading to alternative proofs for and extensions of several existing stability results.<\/jats:p>","DOI":"10.1137\/s0363012900370776","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1922-1945","source":"Crossref","is-referenced-by-count":13,"title":["Trajectory-Based Local Approximations of Ordinary\\ Differential\\ Equations"],"prefix":"10.1137","volume":"41","author":[{"given":"Luc","family":"Moreau","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dirk","family":"Aeyels","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(99)00012-6"},{"key":"R2","volume-title":"Lyapunov exponents and smooth ergodic theory","author":"Barreira Luis","year":"2002"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(77)90101-2"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2644-1"},{"key":"R5","volume-title":"Ordinary differential equations","author":"Hartman Philip","year":"1982"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/1033050"},{"key":"R7","unstructured":"HenryHermes, Asymptotic stabilization via homogeneous approximation, Monogr. 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