Abstract

Kolmogorov-Arnol'd-Moser Theory classically was mainly developed for conservative systems, establishing persistence results for quasi-periodic invariant tori in nearly integrable systems. In this survey we focus on dissipative systems, where similar results hold. In non-conservative settings often parameters are needed for the persistence of invariant tori. When considering families of such dynamical systems bifurcations of quasi-periodic tori may occur. As an example we discuss the quasi-periodic Hopf bifurcation.

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