Numerical exploration of bifurcation phenomena associated with complex instability
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The Hopf-like bifurcation associated with the transition from stability to complex instability of a family of periodic orbits in a Hamiltonian system with three (or more) degrees of freedom is investigated. Numerical techniques to compute the bifurcating objects -periodic orbits or, more generally, 2D isolated invariant tori - are persented. The evolution and further bifurcations of the 2D tori are described. As a model problem, we consider two 4D symplectic mappings, and, as an application, we give some results for a galactic potential.