ON THE DYNAMICS OF A SIMPLE RATIONAL PLANAR MAP

Abstract

The dynamics of the map [Formula: see text] are discussed for various values of its parameters. Despite the simple algebraic structure, this map, recently introduced in the literature, is very rich in nonlinear phenomena. Multiple strange attractors, transitions to chaos via period-doubling bifurcations, quasiperiodicity as well as intermittency, interior crisis, hyperchaos are only a few. In this work, strange attractors, bifurcation diagrams, periodic windows, invariant characteristics are investigated both analytically and numerically.