SRB Measures for A Class of Partially Hyperbolic Attractors in Hilbert spaces
Abstract
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 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.
Keywords
Cite
@article{arxiv.1508.03301,
title = {SRB Measures for A Class of Partially Hyperbolic Attractors in Hilbert spaces},
author = {Zeng Lian and Peidong Liu and Kening Lu},
journal= {arXiv preprint arXiv:1508.03301},
year = {2015}
}