Abstract
Convex dynamical systems are iterated set-valued maps with convex graphs. The closed union of all finite powers of a given convex relation will be called its limit closure. We address the question of transitivity of limit closures and establish a sufficient condition for such transitivity (limit transitivity). We also present examples showing that the limit closure of a general compact convex system is not necessarily transitive. limit closure can be intransitive as well. It is also shown that the restriction of a linear single-valued map to a convex set containing an open neighborhood of the origin is always limit transitive.
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Diamond, P., Vladimirov, A. & Kloeden, P. Transitive Limit Closures of Convex Dynamical Systems. Set-Valued Analysis 6, 113–127 (1998). https://doi.org/10.1023/A:1008636427961
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DOI: https://doi.org/10.1023/A:1008636427961