ABSTRACT
The fi rst part of this chapter is a self-contained introduction to chaos, via the Lozi mappings. The second part presents a rigorous proof of chaos in the Lozi mapping. To maintain uniformity, standard notation is used throughout. Indeed, in Section 3.1 an introduction to chaos via the Lozi maps is presented by means of some quantities defi ned in Chapter 1. In Section 3.2 we discuss ergodic properties of the Lozi mappings, namely, some general properties, construction of invariant measures and their ergodic properties, the Hausdorff dimension and spectra of singularities. Section 3.3 deals with a relatively new result about grammatical complexity for the Lozi mappings including a short introduction to the concepts, defi nitions and methods used to calculate the desired transition rules. In Section 3.4, admissibility conditions with some examples for symbolic sequences of the Lozi map are discussed in some detail. In particular, contracting and expanding foliations and their ordering, the pruning front and admissibility conditions are presented.
