On the Dynamics of a Simple Rational Planar 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.