Strange attractor of the Lozi mappings for the parameter region [[formula omitted]]

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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−b2] which coincides with the closure of the unstable manifold at the fixed point (11+a−b,b1+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.