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arXiv · 2501.15905

Ergodicity of cocyles over 2-dimensional rotations

Nicolas Chevallier·Jean-Pierre Conze
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Abstract

We study recurrence and ergodicity of cocycles with values in R d , d $\ge$ 1, over rotations by badly approximable irrational numbers on T $\rho$ , $\rho$ \> 1. The discontinuities of the functions generating the cocycles also satisfy a Diophantine condition. For simplicity of notation we mainly consider the cases $\rho$ = 2, d = 1 and 2.

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Nicolas Chevallier, Jean-Pierre Conze. 2025-01-27. Ergodicity of cocyles over 2-dimensional rotations. https://arxiv.org/abs/2501.15905

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