【摘 要】
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We study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space.We show several results including(
【机 构】
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BrighamYoungUniversity,USA
【出 处】
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2015年微分方程与动力系统研讨会
论文部分内容阅读
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 H¨older 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 and the splitting is H¨older continuous,then there exists 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.This is a joint work with Zeng Lian and Pei-Dong Liu.
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