Chaos and Shadowing Lemma for Autonomous Systems of Infinite Dimensions
Chaotic Dynamics
2009-11-07 v1 Exactly Solvable and Integrable Systems
Abstract
For finite-dimensional maps and periodic systems, Palmer rigorously proved Smale horseshoe theorem using shadowing lemma in 1988. For infinite-dimensional maps and periodic systems, such a proof was completed by Steinlein and Walther in 1990, and Henry in 1994. For finite-dimensional autonomous systems, such a proof was accomplished by Palmer in 1996. For infinite-dimensional autonomous systems, the current article offers such a proof. First we prove an Inclination Lemma to set up a coordinate system around a pseudo-orbit. Then we utilize graph transform and the concept of persistence of invariant manifold, to prove the existence of a shadowing orbit.
Keywords
Cite
@article{arxiv.nlin/0203024,
title = {Chaos and Shadowing Lemma for Autonomous Systems of Infinite Dimensions},
author = {Yanguang Charles Li},
journal= {arXiv preprint arXiv:nlin/0203024},
year = {2009}
}