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Regular and Chaotic Dynamics, 2011, Volume 16, Issue 1-2, Pages 154–184
DOI: https://doi.org/10.1134/S1560354711010060 (Mi rcd433) 		 
This article is cited in 78 scientific papers (total in 78 papers)

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

Renato Vitoloa, Henk Broerb, Carles Simóc

a 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
Citations (78)
DOI: https://doi.org/10.1134/S1560354711010060
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.
Received: 24.11.2010
Accepted: 15.12.2010
Bibliographic databases:
Document Type: Article
MSC: 37M20, 37C55, 37G30
Language: English
Citation: Renato Vitolo, Henk Broer, Carles Simó, “Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems”, Regul. Chaotic Dyn., 16:1-2 (2011), 154–184
Citation in format AMSBIB
\Bibitem{VitBroSim11}
\by Renato Vitolo, Henk Broer, Carles Sim\'o
\paper Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems
\jour Regul. Chaotic Dyn.
\yr 2011
\vol 16
\issue 1-2
\pages 154--184
\mathnet{http://mi.mathnet.ru/rcd433}
\crossref{https://doi.org/10.1134/S1560354711010060}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2774385}
\zmath{https://zbmath.org/?q=an:1225.37087}
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  • https://www.mathnet.ru/eng/rcd/v16/i1/p154
    • This publication is cited in the following 78 articles:
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