Sinai-Ruelle-Bowen measures for piecewise hyperbolic maps with two directions of instability in three-dimensional spaces

Abstract

A class of piecewise $C^2$ Lozi-like maps in three-dimensional Euclidean spaces is introduced, and the existence of Sinai-Ruelle-Bowen measures is studied, where the dimension of the instability is equal to two. Further, an example with computer simulations is provided to illustrate the theoretical results.