On the relation between topological entropy and restoration entropy
Optimization and Control
2019-01-30 v1 Information Theory
Dynamical Systems
math.IT
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.
Cite
@article{arxiv.1811.11607,
title = {On the relation between topological entropy and restoration entropy},
author = {Christoph Kawan},
journal= {arXiv preprint arXiv:1811.11607},
year = {2019}
}