English

Ergodicity of cocyles over 2-dimensional rotations

Dynamical Systems 2025-01-28 v1

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 ρ\rho , ρ\rho \> 1. The discontinuities of the functions generating the cocycles also satisfy a Diophantine condition. For simplicity of notation we mainly consider the cases ρ\rho = 2, d = 1 and 2.

Keywords

Cite

@article{arxiv.2501.15905,
  title  = {Ergodicity of cocyles over 2-dimensional rotations},
  author = {Nicolas Chevallier and Jean-Pierre Conze},
  journal= {arXiv preprint arXiv:2501.15905},
  year   = {2025}
}