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Degenerate Resonances in Hamiltonian Systems: From Poincaré–Birkhoff Chains to Vortex Pairs and Kármán Vortex Streets

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For Hamiltonian systems with two degrees of freedom, close to nonlinear integrable systems, we discuss rearrangements in the degenerate resonance zones in terms of the averaged system normalized near the resonance. For degeneracy order n = 3 we describe typical rearrangements of phase portraits connected with passage from Poincaré–Birkhoff chains to vortex pairs and Kármán vortex streets. Bibliography: 16 titles.

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Authors and Affiliations

  1. University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    A. A. Karabanov

  2. Lobachevski State University of Nizhni Novgorod, 23, Gagarina pr., Nizhni Novgorod, 603950, Russia

    A. D. Morozov

Authors
  1. A. A. Karabanov
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  2. A. D. Morozov
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Correspondence to A. D. Morozov.

Additional information

Translated from Problemy Matematicheskogo Analiza 85, June 2016, pp. 147-151.

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Karabanov, A.A., Morozov, A.D. Degenerate Resonances in Hamiltonian Systems: From Poincaré–Birkhoff Chains to Vortex Pairs and Kármán Vortex Streets. J Math Sci 219, 155–159 (2016). https://doi.org/10.1007/s10958-016-3092-7

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  • DOI: https://doi.org/10.1007/s10958-016-3092-7

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