Local large deviation principle for Smale spaces
Dynamical Systems
2025-10-02 v1 Probability
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.
Cite
@article{arxiv.2510.00972,
title = {Local large deviation principle for Smale spaces},
author = {David Parmenter},
journal= {arXiv preprint arXiv:2510.00972},
year = {2025}
}