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Limit theorems for non-hyperbolic automorphisms of the torus

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Abstract

We prove the Donsker and Strassen invariance principles and other results for ergodic sums associated to regular functions for non-hyperbolic automorphisms of the torus. For this we use arithmetical and geometrical considerations which allow us to apply Gordin’s method.

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Authors and Affiliations

  1. IRMAR, Université de Rennes I, 35042, Rennes Cedex, France

    Stéphane Le Borgne

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  1. Stéphane Le Borgne
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Correspondence to Stéphane Le Borgne.

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Le Borgne, S. Limit theorems for non-hyperbolic automorphisms of the torus. Isr. J. Math. 109, 61–73 (1999). https://doi.org/10.1007/BF02775027

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  • DOI: https://doi.org/10.1007/BF02775027

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