We give necessary conditions for a set to be topologically transitive attractor of an analytic plane flow using topological characterization of ω-limit sets and the concept of upper semi-continuity of multi valued maps.
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].
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