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

Ergodicity of certain cocycles over certain interval exchanges

Pages: 2523 - 2529, Volume 33, Issue 6, June 2013      doi:10.3934/dcds.2013.33.2523

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David Ralston - SUNY College at Old Westbury, Mathematics/CIS Department, P.O. Box 210, Old Westbury, NY 11568, United States (email)
Serge Troubetzkoy - Aix-Marseille University, CNRS, CPT, IML, Frumam, 13288 Marseille Cedex 09, France (email)

Abstract: We show that for odd-valued piecewise-constant skew products over a certain two parameter family of interval exchanges, the skew product is ergodic for a full-measure choice of parameters.

Keywords:  Ergodicity, cocycle, interval exchange, essential value, infinite ergodic theory.
Mathematics Subject Classification:  Primary: 37A20, 37E10, 37A25; Secondary: 37E35.

Received: January 2012;      Revised: October 2012;      Available Online: December 2012.