Local large deviation principle for Smale spaces

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.