2002/03/13 by Yanguang Charles Li, Yanguang Li · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #nlin.CD #nlin.SI
paper · pdf · doi:10.1023/b:jody.0000010062.09599.d8
arxiv created 2002/03/13 · openalex publication_date 2003/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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.