Localization of the Chain Recurrent set using Shape theory and Symbolical Dynamics

Abstract

<jats:title>Abstract</jats:title><jats:p>The main aim of this paper is localization of the chain recurrent set in shape theoretical framework. Namely, using the intrinsic approach to shape from [1] we present a result which claims that under certain conditions the chain recurrent set preserves local shape properties. We proved this result in [2] using the notion of a proper covering. Here we give a new proof using the Lebesque number for a covering and verify this result by investigating the symbolical image of a couple of systems of differential equations following [3].</jats:p>