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

Zeng Lian; Peidong Liu; Kening Lu

doi:10.3934/dcds.2017164

Article Contents

2017, Volume 37, Issue 7: 3905-3920. Doi: 10.3934/dcds.2017164

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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: August 2017

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 37D30, 37C40.

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References

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