The geometric structure of strange attractors in the Lozi map (Q1288379)

The Lozi map \(T_{a,b}(x,y):= (1-a| x|+y,bx)\) is a typical two-dimensional map. The authors study the structure of the strange attractors for the Lozi map. In their previous works the authors proved that, when \(b<0\), there exists an open set \(E\) such that, if \((a,b)\in E\), the corresponding map exhibits a strange attractor \(\Lambda_{a,b}\) and the basin \(b(\Lambda_{a,b})\) of \(\Lambda_{a,b}\) contains a neighborhood of itself, and the unions of the transversal homoclinic points and weak transversal homoclinic points are dense in \(\Lambda_{a,b}\). The present paper is devoted to the further investigation of the structure of the strange attractors for the Lozi map.