Ergodicity of certain cocycles over certain interval exchanges

David Ralston; Serge Troubetzkoy

doi:10.3934/dcds.2013.33.2523

Article Contents

2013, Volume 33, Issue 6: 2523-2529. Doi: 10.3934/dcds.2013.33.2523

This issue Previous Article Population dynamical behavior of Lotka-Volterra cooperative systems with random perturbations Next Article Global well-posedness of the Chern-Simons-Higgs equations with finite energy

Ergodicity of certain cocycles over certain interval exchanges

David Ralston^1, and
Serge Troubetzkoy^2,

1.
SUNY College at Old Westbury, Mathematics/CIS Department, P.O. Box 210, Old Westbury, NY 11568
2.
Aix-Marseille University, CNRS, CPT, IML, Frumam, 13288 Marseille Cedex 09

Received: December 31, 2011

Revised: September 30, 2012

Published: June 2013

Abstract Related Papers Cited by

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:

Mathematics Subject Classification: Primary: 37A20, 37E10, 37A25; Secondary: 37E35.

Citation:

Related Papers

Cited by

References

[1]	J. Chaika and P. Hubert, Ergodicity of skew products over interval exchange transformations, in preparation.
[2]	J.-P. Conze, Recurrence, ergodicity and invariant measures for cocycles over a rotation, in "Ergodic Theory" Contemp. Math. AMS, 485 (2009), 45-70.doi: 10.1090/conm/485/09492.
[3]	J.-P. Conze and K. Frączek, Cocycles over interval exchange transformations and multivalued Hamiltonian flows, Advances in Mathematics, 226 (2011), 4373-4428.
[4]	S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Annals of Mathematics, 124 (1986), 293-311.
[5]	A. Ya. Khinchin and A. Ya., "Continued Fractions," Dover Publications Inc., Mineola, NY, 1997.
[6]	L. Kuipers and H. Niederreiter, "Uniform Distribution of Sequences," Wiley-Interscience, New York, 1974.
[7]	K. Schmidt, "Cocycles on Ergodic Transformation Groups," Macmillan Lectures in Mathematics, 1, Delhi 1977.