2013, 33(6): 2523-2529. doi: 10.3934/dcds.2013.33.2523

Ergodicity of certain cocycles over certain interval exchanges

1. 

SUNY College at Old Westbury, Mathematics/CIS Department, P.O. Box 210, Old Westbury, NY 11568, United States

2. 

Aix-Marseille University, CNRS, CPT, IML, Frumam, 13288 Marseille Cedex 09, France

Received  January 2012 Revised  October 2012 Published  December 2012

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.
Citation: David Ralston, Serge Troubetzkoy. Ergodicity of certain cocycles over certain interval exchanges. Discrete & Continuous Dynamical Systems - A, 2013, 33 (6) : 2523-2529. doi: 10.3934/dcds.2013.33.2523
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, 485 (2009), 45. 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.

[4]

S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials,, Annals of Mathematics, 124 (1986), 293.

[5]

A. Ya. Khinchin and A. Ya., "Continued Fractions,", Dover Publications Inc., (1997).

[6]

L. Kuipers and H. Niederreiter, "Uniform Distribution of Sequences,", Wiley-Interscience, (1974).

[7]

K. Schmidt, "Cocycles on Ergodic Transformation Groups,", Macmillan Lectures in Mathematics, 1 (1977).

show all references

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, 485 (2009), 45. 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.

[4]

S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials,, Annals of Mathematics, 124 (1986), 293.

[5]

A. Ya. Khinchin and A. Ya., "Continued Fractions,", Dover Publications Inc., (1997).

[6]

L. Kuipers and H. Niederreiter, "Uniform Distribution of Sequences,", Wiley-Interscience, (1974).

[7]

K. Schmidt, "Cocycles on Ergodic Transformation Groups,", Macmillan Lectures in Mathematics, 1 (1977).

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