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Limit theorems for skew translations

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  • Bufetov, Bufetov-Forni and Bufetov-Solomyak have recently proved limit theorems for translation flows, horocycle flows and tiling flows, respectively. We present here analogous results for skew translations of a torus.
    Mathematics Subject Classification: Primary: 37A50; Secondary: 11F27, 60F05, 37D40, 28D05.

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  • [1]

    A. Bufetov, Limit theorems for translation flows, Ann. of Math. (2), 179 (2014), 431-499.doi: 10.4007/annals.2014.179.2.2.

    [2]

    A. Bufetov and G. Forni, Limit theorems for horocycle flows, arXiv:1104.4502.

    [3]

    A. Bufetov and B. Solomyak, Limit theorems for self-similar tilings, Comm. Math. Phys., 319 (2013), 761-789.doi: 10.1007/s00220-012-1624-7.

    [4]

    D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations I. Convex bodies, Geom. Funct. Anal., 24 (2014), 85-115.doi: 10.1007/s00039-014-0254-y.

    [5]

    D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations II. Boxes, arXiv:1211.4323.

    [6]

    F. Cellarosi, Limiting curlicue measures for theta sums, Ann. Inst. Henri Poincaré Probab. Stat., 47 (2011), 466-497.doi: 10.1214/10-AIHP361.

    [7]

    A. Fedotov and F. Klopp, An exact renormalization formula for Gaussian exponential sums and applications, Amer. J. Math., 134 (2012), 711-748.doi: 10.1353/ajm.2012.0016.

    [8]

    L. Flaminio and G. Forni, Equidistribution of nilflows and applications to theta sums, Ergodic Theory Dynam. Systems, 26 (2006), 409-433.doi: 10.1017/S014338570500060X.

    [9]

    W. B. Jurkat and J. W. Van Horne, The proof of the central limit theorem for theta sums, Duke Math. J., 48 (1981), 873-885.doi: 10.1215/S0012-7094-81-04848-1.

    [10]

    W. B. Jurkat and J. W. Van Horne, On the central limit theorem for theta series, Michigan Math. J., 29 (1982), 65-77.doi: 10.1307/mmj/1029002615.

    [11]

    W. B. Jurkat and J. W. Van Horne, The uniform central limit theorem for theta sums, Duke Math. J., 50 (1983), 649-666.doi: 10.1215/S0012-7094-83-05030-5.

    [12]

    H. Kesten, Uniform distribution mod 1, Ann. of Math. (2), 71 (1960), 445-471.doi: 10.2307/1969938.

    [13]

    H. Kesten, Uniform distribution mod 1. II, Acta Arith., 7 (1961/1962), 355-380.

    [14]

    J. Marklof, Limit theorems for theta sums, Duke Math. J., 97 (1999), 127-153.doi: 10.1215/S0012-7094-99-09706-5.

    [15]

    J. Marklof, Almost modular functions and the distribution of $n^2 x$ modulo one, Int. Math. Res. Not., 39 (2003), 2131-2151.doi: 10.1155/S1073792803130292.

    [16]

    J. Marklof, Pair correlation densities of inhomogeneous quadratic forms, Ann. of Math. (2), 158 (2003), 419-471.doi: 10.4007/annals.2003.158.419.

    [17]

    Y. G. Sinai and C. Ulcigrai, A limit theorem for Birkhoff sums of nonintegrable functions over rotations, in Geometric and Probabilistic Structures in Dynamics, Contemp. Math., 469, Amer. Math. Soc., Providence, RI, 2008, 317-340.doi: 10.1090/conm/469/09174.

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