Monotonicity of the Lozi Family and the Zero Entropy Locus

Abstract

Ishii and Sands showed the monotonicity of the Lozi family La,b in a C1 neighborhood of a-axis in the a-b parameter space. We show the monotonicity of the entropy in the vertical direction around a=2 and in some other directions for 1<a≤2. Also we give some rigorous and numerical results for the parameters at which the Lozi family has zero entropy.