Strange attractor of the Lozi mappings for the parameter region [0 IF 1.2 3区 数学 Q1 MATHEMATICS Journal of Mathematical Analysis and Applications Pub Date : 2024-10-31 DOI:10.1016/j.jmaa.2024.129018 Khadija Ben Rejeb

Abstract

In this paper, we give a mathematical proof to the existence of a strange attractor for the Lozi mapping L. More precisely, we prove that L has a unique strange attractor for the parameter region [$0<b<1,b+1<a<2-\frac{b}{2}$] which coincides with the closure of the unstable manifold at the fixed point $(\frac{1}{1+a-b},\frac{b}{1+a-b})$. This extends a result obtained by (M. Misiurewicz, Strange attractor for the Lozi mapping, Ann.N.Y. Acad. Sci. 357, (1980), pp. 348-358). On the other hand, we study the dynamical behavior of the map L on its strange attractor and we prove that it is Li-Yorke chaotic. MSC 2010 Primary: 37D45, 37E30.