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arXiv · 2510.00972

Local large deviation principle for Smale spaces

David Parmenter
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Abstract

Large deviation principles for hyperbolic systems are well studied and provide exponential rates for the deviations of Birkhoff averages from their limit. This short article presents a local large deviation principle for Smale spaces, in particular studying the rate functions of deviations with respect to conditional Gibbs measures supported on local unstable manifolds. The proof builds on a result due to Kifer and pressure growth estimates due to Parmenter and Pollicott.

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David Parmenter. 2025-10-01. Local large deviation principle for Smale spaces. https://arxiv.org/abs/2510.00972

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