Local limit theorem for nonuniformly partially hyperbolic skew-products, and Farey sequences

Sebastien Gouezel

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arXiv · math/0703670

Local limit theorem for nonuniformly partially hyperbolic skew-products, and Farey sequences

Sebastien Gouezel

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Abstract

We study skew-products of the form (x,ω)\mapsto (Tx, ω+ϕ(x)) where T is a nonuniformly expanding map on a space X, preserving a (possibly singular) probability measure \tildeμ, and ϕ:X\to S^1 is a C^1 function. Under mild assumptions on \tildeμand ϕ, we prove that such a map is exponentially mixing, and satisfies the central and local limit theorems. These results apply to a random walk related to the Farey sequence, thereby answering a question of Guivarc'h and Raugi.

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BibTeX RIS

Sebastien Gouezel. 2007-03-22. Local limit theorem for nonuniformly partially hyperbolic skew-products, and Farey sequences. https://arxiv.org/abs/math/0703670

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