On the relation between topological entropy and restoration entropy

Christoph Kawan

doi:10.3390/e21010007

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arXiv · 1811.11607

On the relation between topological entropy and restoration entropy

Christoph Kawan

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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 which 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.

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Christoph Kawan. 2018-11-28. On the relation between topological entropy and restoration entropy. https://doi.org/10.3390/e21010007

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