کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4609484 | 1338513 | 2016 | 72 صفحه PDF | دانلود رایگان |
In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic and the system is topological mixing and the splitting is Hölder continuous, then there exists a unique SRB measure which is mixing; (iii) if the attractor is uniformly hyperbolic and the system is non-wondering and the splitting is Hölder continuous, then there exist at most finitely many SRB measures; (iv) for a given hyperbolic measure, there exist at most countably many ergodic components whose basin contains an observable set.
Journal: Journal of Differential Equations - Volume 261, Issue 2, 15 July 2016, Pages 1532–1603