95-440 Stathis Tompaidis

Approximation of invariant surfaces by periodic orbits in high-dimensional maps. Some rigorous results. (64K, TeX) Oct 2, 95

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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.

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