BIFURCATION PHENOMENA FOR TWO-DIMENSIONAL PIECEWISE LINEAR MAPS

摘要

We consider a four-parameter family of two-dimensional piecewise linear endomorphisms as a mathematical model for the investigations of different types of attractors and their bifurcations in piecewise linear case. Main attention is paid to a flip bifurcation. We show that it can result in the appearance of attracting point cycles of any even periods, as well as of attracting cycles of chaotic sets of any even periods. Further bifurcations are discussed; it is shown that some of them appear to be accompanied by the so-called "rare points" phenomenon. This text is an extended version of [7].