Circle Like Strange Attractor in a Piecewise Smooth Map*

we explore the dynamics of a piecewise linear normal form map under the condition that the map is contractive in one compartment and expansive in the other. In particular, we analyze the transition from a mode-locked periodic orbit to a chaotic orbit. It occurs through the following sequence: first homoclinic contact followed by homoclinic intersection, which is again followed by a second homoclinic contact. We have shown that after the second homoclinic contact, a circular-shaped strange attractor with an infinite number of non-smooth folds is created. The mechanism of this chaotic behavior is explained in terms of tangencies with the stable foliation of the saddle fixed point.