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

Smooth stabilizers for measures on the torus

Pages: 43 - 58, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.43

       Abstract        References        Full Text (415.2K)       Related Articles       

Aaron W. Brown - Department of Mathematics, The Pennsylvania State University, State College, PA 16802, United States (email)

Abstract: For a dissipative Anosov diffeomorphism $f$ of the 2-torus, we give examples of $f$-invariant measures $\mu$ such that the group of $\mu$-preserving diffeomorphisms is virtually cyclic.

Keywords:  Anosov diffeomorphisms, invariant measures, group actions, rigidity, hyperbolic dynamics.
Mathematics Subject Classification:  Primary: 37C40, 37D20; Secondary: 37E30.

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