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Equipartition of the eigenfunctions of quantized ergodic maps on the torus

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Abstract

We give a simple proof of the equipartition of the eigenfunctions of a class of quantized ergodic area-preserving maps on the torus. Examples are the irrational translations, the skew translations, the hyperbolic automorphisms and some of their perturbations.

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Author notes

  1. A. Bouzouina

    Present address: CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

  2. S. De Bièvre

    Present address: UFR de Mathématiques, Université Paris VII, Paris, France

Authors and Affiliations

  1. Laboratoire de Physique Théorique et Mathématique Université Paris VII, 2 place Jussieu, F-75251, Paris Cedex 05, France

    A. Bouzouina & S. De Bièvre

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  1. A. Bouzouina
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  2. S. De Bièvre
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Communicated by Ya.G. Sinai

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Bouzouina, A., De Bièvre, S. Equipartition of the eigenfunctions of quantized ergodic maps on the torus. Commun.Math. Phys. 178, 83–105 (1996). https://doi.org/10.1007/BF02104909

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  • DOI: https://doi.org/10.1007/BF02104909

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