CHARACTERISTICS OF DISCONTINUOUS AND NONINVERTIBLE 2-D MAPS

This paper presents a review on recent investigations about the classic dynamics general features of the noninvertible and discontinuous two-dimensional maps. For concreteness we consider a system with phase space divided into two distinct but complementary regions R1 and R2. They are the domains of the map functions f1(x) and f2(x), respectively. The common features of the systems include: the stochastic web formed by image set of discontinuous borderline; phase collapse caused by the irreversibility (quasi-dissipation); fat fractal forbidden web; riddled-like attraction basin and the induced unpredictability of attractors. Several different cases where f1(x) and f2(x) are both area preserving; one is area preserving and another is dissipative; or both are dissipative have been studied. In all the cases the dynamics features can be displayed, however with different characteristics. The features are interesting and can be verified experimentally.