- 95-440 Stathis Tompaidis
- Approximation of invariant surfaces by periodic orbits in high-dimensional
maps. Some rigorous results.
Oct 2, 95
(auto. generated ps),
of related papers
Abstract. The existence of an invariant surface in high-dimensional systems greatly
influences the behavior in a neighborhood of the invariant surface. We
prove theorems that explain the behavior of periodic orbits in the
vicinity of an invariant surface for symplectic maps and quasi-periodic
perturbations of symplectic maps.
Our results allow for efficient numerical algorithms that can
serve as an indication for the breakdown of invariant surfaces.