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Entropy 2019, 21(1), 7; https://doi.org/10.3390/e21010007

On the Relation between Topological Entropy and Restoration Entropy

Fakultät für Informatik und Mathematik, Universität Passau, Innstraße 33, 94032 Passau, Germany
Received: 28 November 2018 / Revised: 17 December 2018 / Accepted: 20 December 2018 / Published: 23 December 2018
(This article belongs to the Special Issue Entropy in Networked Control)
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Abstract

In the context of state estimation under communication constraints, several notions of dynamical entropy play a fundamental role, among them: topological entropy and restoration entropy. In this paper, we present a theorem that demonstrates that for most dynamical systems, restoration entropy strictly exceeds topological entropy. This implies that robust estimation policies in general require a higher rate of data transmission than non-robust ones. The proof of our theorem is quite short, but uses sophisticated tools from the theory of smooth dynamical systems. View Full-Text
Keywords: topological entropy; restoration entropy; state estimation under communication constraints; SRB measures; Anosov diffeomorphisms topological entropy; restoration entropy; state estimation under communication constraints; SRB measures; Anosov diffeomorphisms
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kawan, C. On the Relation between Topological Entropy and Restoration Entropy. Entropy 2019, 21, 7.

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