Journal of Statistical Physics

, Volume 101, Issue 1–2, pp 321–356

On Two-Dimensional Area-Preserving Diffeomorphisms with Infinitely Many Elliptic Islands

  • S. V. Gonchenko
  • L. P. Shilnikov

DOI: 10.1023/A:1026418323000

Cite this article as:
Gonchenko, S.V. & Shilnikov, L.P. Journal of Statistical Physics (2000) 101: 321. doi:10.1023/A:1026418323000


We consider two-parameter families of Cr-smooth, r≥6, two-dimensional area-preserving diffeomorphisms that have structurally unstable simplest heteroclinic cycles. We find the conditions when diffeomorphisms under consideration possess infinitely many periodic generic elliptic points and elliptic islands.

area-preserving diffeomorphisms structurally unstable heteroclinic cycle elliptic periodic point elliptic island the conservative Henon map 

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • S. V. Gonchenko
    • 1
  • L. P. Shilnikov
    • 2
  1. 1.Inst. for Appl. Math. and Cyb.Nizhnii NovgorodRussia
  2. 2.Inst. for Appl. Math. and Cyb.Nizhnii NovgorodRussia

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