Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors

We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire Received: 1 September 1996 / Accepted: 16 April 1997