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

Renato Vitolo^a, Henk Broer^b, Carles Simó<sup>c

a</sup> College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, North Park Road, Exeter, EX4 4QF, UK
^b Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, PO Box 407, 9700 AK Groningen, The Netherlands
^c Departament de Matemàtica Aplicada i Anàlisi Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

Abstract: 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.

MSC: 37M20, 37C55, 37G30

Received: 24.11.2010
Accepted: 15.12.2010

Language: English

DOI: 10.1134/S1560354711010060

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