Strange attractors in the orientation-preserving Lozi map

In this paper, we prove that the Lozi map T-a,T-b(x, y) = (1 - a\x\ + y, bx ), when b < 0, there exists an open set E in the parameter plane such that if (a, b) is an element of E, the corresponding map exhibits a strange attr actor Lambda(a,b) and the basin B(Lambda(a.b)) Of Lambda(a,b) contains a ne ighbourhood of itself. Furthermore, we prove that the unions of the transve rsal homoclinic points;and weak transversal homoclinic points are dense in Lambda(a,b). (C) 1998 Elsevier Science Ltd. All rights reserved.