WIAS Preprint No. 791, (2002)

Infinitely many elliptic periodic orbits in four-dimensional symplectic maps with a homoclinic tangency


  • Gonchenko, Sergey V.
  • Shilnikov, Leonid P.
  • Turaev, Dmitry

2010 Mathematics Subject Classification

  • 37G25 37J45 37J20


  • Hamiltonian dynamics, Henon map, renormalization


We show that systems having infinitely many coexisting generic 2-elliptic periodic orbits are dense among the four-dimensional symplectic maps with an orbit of homoclinic tangency to a saddle-focus.

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