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Perturbative renormalization analysis of the Poincaré–Birkhoff resonance in 2-D symplectic map

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  • Kano, Hiroyuki
  • Nozaki, Kazuhiro

Abstract

A perturbative analysis based on the renormalization method shows that the period-four torus near an elliptic fixed point of the radially twist map goes through not only the Poincaré–Birkhoff bifurcation but also an exchange-type bifurcation and the global ballooning of resonant islands. The appearance of the exchange-type bifurcation is found to be closely connected to the Suris’ integrable maps.

Suggested Citation

  • Kano, Hiroyuki & Nozaki, Kazuhiro, 2007. "Perturbative renormalization analysis of the Poincaré–Birkhoff resonance in 2-D symplectic map," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 215-223.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:215-223
    DOI: 10.1016/j.chaos.2005.10.107
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