A note on  partially hyperbolic attractors: Entropy conjecture and SRB measures

Peidong Liu; Kening Lu

doi:10.3934/dcds.2015.35.341

Article Contents

2015, Volume 35, Issue 1: 341-352. Doi: 10.3934/dcds.2015.35.341

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A note on partially hyperbolic attractors: Entropy conjecture and SRB measures

Peidong Liu^1, and
Kening Lu^2,

1.
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871
2.
Department of Mathematics, Brigham Young University, Provo, Utah 84602

Received: August 31, 2013

Revised: May 31, 2014

Published: December 2014

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Abstract

In this note we show that, for a class of partially hyperbolic $C^r$ ($r \geq 1$) diffeomorphisms, (1) Shub's entropy conjecture holds true; (2) SRB measures exist as zero-noise limits.

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Mathematics Subject Classification: Primary: 37D30; Secondary: 37C40, 37H15.

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