A note on the large deviations for piecewise expanding multidimensional maps

TL;DR

This paper establishes the large deviation principle for higher-dimensional piecewise expanding maps using a modified functional approach, advancing the understanding of their probabilistic behavior.

Contribution

It introduces a slightly modified functional approach to prove large deviations for multidimensional piecewise expanding maps, extending previous one-dimensional results.

Findings

Large deviation principle is proven for multidimensional maps.

The functional approach of Hennion and Hervé is adapted for higher dimensions.

Results contribute to the theoretical understanding of complex dynamical systems.

Abstract

We provide the large deviation principle for higher dimensional piecewise expanding maps and by using the functional approach of Hennion and Herv\'e, slightly modified.