Stathis Tompaidis
Approximation of invariant surfaces by periodic orbits in high-dimensional
maps. Some rigorous results.
(64K, TeX)

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.