This book is a comprehensive collection of known results about the Lozi map, a piecewise-affine version of the Henon map. Henon map is one of the most studied examples in dynamical systems and it attracts a lot of attention from researchers, however it is difficult to analyze analytically. Simpler structure of the Lozi map makes it more suitable for such analysis. The book is not only a good introduction to the Lozi map and its generalizations, it also summarizes of important concepts in dynamical systems theory such as hyperbolicity, SRB measures, attractor types, and more.
Table of Contents
Comprehensive Review of Hyperbolicity, Ergodicity, and Chaos. Reality of Chaos in the Hénon Mapping. Dynamical Properties of the Lozi Mappings. Dynamical Properties of Modified and Generalized Lozi Mappings. Real and Mathematical Applications of Lozi Mappings.