Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 341 - 352, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.341

       Abstract        References        Full Text (386.3K)       Related Articles       

Peidong Liu - LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China (email)
Kening Lu - Department of Mathematics, Brigham Young University, Provo, Utah 84602, United States (email)

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.

Keywords:  Partially hyperbolic attractors, entropy conjecture, SRB measures, random perturbations.
Mathematics Subject Classification:  Primary: 37D30; Secondary: 37C40, 37H15.

Received: September 2013;      Revised: June 2014;      Available Online: August 2014.