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1996 Approximation of invariant surfaces by periodic orbits in high-dimensional maps: some rigorous results
Stathis Tompaidis
Experiment. Math. 5(3): 197-209 (1996).

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 predict the behavior of periodic orbits in the vicinity of an invariant surface on which the motion is conjugate to a Diophantine rotation for symplectic maps and quasiperiodic 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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Stathis Tompaidis. "Approximation of invariant surfaces by periodic orbits in high-dimensional maps: some rigorous results." Experiment. Math. 5 (3) 197 - 209, 1996.

Information

Published: 1996
First available in Project Euclid: 17 March 2003

zbMATH: 0867.58056
MathSciNet: MR1426448

Subjects:
Primary: 58F27
Secondary: 34C25 , 34C30

Rights: Copyright © 1996 A K Peters, Ltd.

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Vol.5 • No. 3 • 1996
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