On the Dynamics of a Simple Rational Planar Map

The dynamics of the map are discussed for various values of it’s parameters. Despite the simple algebraic structure, this map, recently introduced in the literature, is very rich in non-linear phenomena. Multiple strange attractors, transitions to chaos via period doubling bifurcations, quasiperiodicity as well as intermittency, interior crisis, hyper-chaos are only a few. In this work, strange attractors, bifurcation diagrams, periodic windows, invariant characteristics are investigated both analytically and numerically.