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Chaos and Shadowing Lemma for Autonomous Systems of Infinite Dimensions

Yanguang Charles Li
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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.

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Yanguang Charles Li. 2002-03-13. Chaos and Shadowing Lemma for Autonomous Systems of Infinite Dimensions. https://doi.org/10.1023/b%3Ajody.0000010062.09599.d8

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