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Ergodicity of certain cocycles over certain interval exchanges

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


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    J. Chaika and P. HubertErgodicity of skew products over interval exchange transformations, in preparation.


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    J.-P. Conze and K. Frączek, Cocycles over interval exchange transformations and multivalued Hamiltonian flows, Advances in Mathematics, 226 (2011), 4373-4428.


    S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Annals of Mathematics, 124 (1986), 293-311.


    A. Ya. Khinchin and A. Ya., "Continued Fractions," Dover Publications Inc., Mineola, NY, 1997.


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


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

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