ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

We investigate global bifurcations in the phase space of a biparametric two-dimensional map, the standard map, derived from a model for the periodically kicked mechanical rotor. This mathematical model presents a wide assortment of dynamical phenomena, being an adequate paradigm for studying several fundamental features such as multistability, crises, and chaotic transients. Starting with the conservative case of the map, we illustrate the mechanisms of creation, merging and destruction of typical chaotic attractors, as dissipation builds up. Through the characterization of an interior, a merging and a boundary crisis, we study the crucial role played by important invariant structures, such as unstable periodic orbits and their invariant manifolds, in the mechanisms by which the phase space is globally transformed. Also, special attention is payed to the effects of the dissipative and the forcing parameters in the feature of multistability.