Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems

    2011, Volume 16, Numbers 1-2, pp.  154-184

    Author(s): Vitolo R., Broer H. W., Simó C.

    This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, saddle-node and period-doubling type.
    Keywords: bifurcations, invariant tori, resonances, KAM theory
    Citation: Vitolo R., Broer H. W., Simó C., Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems, Regular and Chaotic Dynamics, 2011, Volume 16, Numbers 1-2, pp. 154-184
    DOI: 10.1134/S1560354711010060



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