Journal of Nonlinear Science

, Volume 12, Issue 1, pp 27–58

Multidimensional Symplectic Separatrix Maps

  • D. Treschev
Article

DOI: 10.1007/s00332-001-0460-2

Cite this article as:
Treschev, D. J. Nonlinear Sci. (2002) 12: 27. doi:10.1007/s00332-001-0460-2

Summary.

We consider an a priori unstable (initially hyperbolic) near-integrable Hamiltonian system in a neighborhood of stable and unstable asymptotic manifolds of a family of hyperbolic tori. Such a neighborhood contains the most chaotic part of the dynamics. The main result of the paper is the construction of the separatrix map as a convenient tool for the studying of such dynamics. We present evidence that the separatrix map combined with the method of anti-integrable limit can give a large class of chaotic trajectories as well as diffusion trajectories.

Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • D. Treschev
    • 1
  1. 1.Department of Mechanics and Mathematics, Moscow State University, Vorob'evy Gory, Moscow 119899, RussiaRU