# American Institute of Mathematical Sciences

July  2017, 37(7): 3905-3920. doi: 10.3934/dcds.2017164

## Existence of SRB measures for a class of partially hyperbolic attractors in banach spaces

 1 School of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China 2 School of Mathematical Sciences, Peking University, Beijing 100871, China 3 Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA

Received  August 2016 Revised  February 2017 Published  April 2017

Fund Project: This work was partially supported by NSFC (11331007, 11541003, and 11671279), and NSF (1413603).

In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure.

Citation: Zeng Lian, Peidong Liu, Kening Lu. Existence of SRB measures for a class of partially hyperbolic attractors in banach spaces. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3905-3920. doi: 10.3934/dcds.2017164
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