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	SRB measures for a class of partially hyperbolic attractors in Hilbert spaces
	Lian, Zeng ; Liu, Peidong ; Lu, Kening
	2016
关键词	SRB measure Infinite dimensional dynamical systems Partial hyperbolicity Absolute continuity Stable foliation Observable sets CONTINUOUS INVARIANT-MEASURES ONE-DIMENSIONAL MAPS DYNAMICAL-SYSTEMS CENTRAL DIRECTION ERGODIC-THEORY AXIOM ENTROPY
英文摘要	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 Holder 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 Holder 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. (C) 2016 Elsevier Inc. All rights reserved.; CNSF [11331007]; NSF [1413603]; SCI(E); ARTICLE; zenglian@gmail.com; lpd@pku.edu.cn; klu@math.byu.edu; 2; 1532-1603; 261
语种	英语
出处	SCI
出版者	JOURNAL OF DIFFERENTIAL EQUATIONS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/438087]
专题	数学科学学院
推荐引用方式 GB/T 7714	Lian, Zeng,Liu, Peidong,Lu, Kening. SRB measures for a class of partially hyperbolic attractors in Hilbert spaces. 2016-01-01.

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