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

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dc.creatorGouezel, Sebastien
dc.date2007-03-22
dc.date.accessioned2026-07-07T07:53:16Z
dc.date.available2026-07-07T07:53:16Z
dc.descriptionWe 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.
dc.description55 pages
dc.identifierhttps://arxiv.org/abs/math/0703670
dc.identifierhttp://arxiv.org/abs/math/0703670
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126188
dc.subjectDynamical Systems
dc.subject37A25, 37A30, 37A50, 37D25, 37D30
dc.titleLocal limit theorem for nonuniformly partially hyperbolic skew-products, and Farey sequences
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