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Mixing properties of generalized T,T−1 transformations

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Abstract

We study mixing properties of generalized T,T−1 transformations. We discuss two mixing mechanisms. In the case the fiber dynamics is mixing, it is sufficient that the driving cocycle is small with small probability. In the case the fiber dynamics is only assumed to be ergodic, one needs to use the shearing properties of the cocycle. Applications include the central limit theorem for sufficiently fast mixing systems and the estimates on deviations of ergodic averages.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Dmitry Dolgopyat, Changguang Dong & Adam Kanigowski

  2. Department of Mathematical Sciences, Yeshiva University, New York, NY, 10016, USA

    Peter Nándori

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  1. Dmitry Dolgopyat
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  2. Changguang Dong
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  3. Adam Kanigowski
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  4. Peter Nándori
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Correspondence to Dmitry Dolgopyat.

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Dolgopyat, D., Dong, C., Kanigowski, A. et al. Mixing properties of generalized T,T−1 transformations. Isr. J. Math. 247, 21–73 (2022). https://doi.org/10.1007/s11856-022-2289-3

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