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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received March 26, 2001; accepted November 5, 2001
Rights and permissions
About this article
Cite this article
Treschev, D. Multidimensional Symplectic Separatrix Maps. J. Nonlinear Sci. 12, 27–58 (2002). https://doi.org/10.1007/s00332-001-0460-2
Issue Date:
DOI: https://doi.org/10.1007/s00332-001-0460-2