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Calculating Topological Entropy

Journal of Statistical Physics, 1997
This paper deals with the attempt to find effective algorithms for calculating the topological entropy of piecewise monotone maps of the interval having more than three pieces. The original motivation for the algorithms described in this paper is based on the following fact: If \(g\) is a piecewise monotone continuous function on the unit interval ...
Baldwin, Stewart L., Slaminka, Edward E.
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A Note on Topological Feedback Entropy and Invariance Entropy [PDF]

Systems and Control Letters, 2013
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Christoph Kawan, Girish Nair, Fritz Colonius   +2 more
exaly   +3 more sources

TOPOLOGICAL ENTROPY VERSUS GEODESIC ENTROPY

International Journal of Mathematics, 1994
Using Yomdin's Theorem [8], we show that for a compact Riemannian manifold M, the geodesic entropy — defined as the exponential growth rate of the average number of geodesic segments between two points — is ≤ the topological entropy of the geodesic flow of M.
Paternain, Gabriel P., Paternain, Miguel
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Topological Sequence Entropy and Chaos

International Journal of Bifurcation and Chaos, 2014
A dynamical system is called a null system, if the topological sequence entropy along any strictly increasing sequence of non-negative integers is 0. Given 0 ≤ p ≤ q ≤ 1, a dynamical system is [Formula: see text] chaotic, if there is an uncountable subset in which any two different points have trajectory approaching time set with lower density p and ...
Xin Liu, Huoyun Wang, Heman Fu
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Topological R-Entropy and Topological Entropy of Free Semigroup Actions

Journal of Mathematical Analysis and Applications, 2019
The paper introduces the notion of topological \(r\)-entropy for a free semigroup action. A link between the topological \(r\)-entropy and the topological entropy of a continuous map of a compact metric space \((X, d)\) is presented. Let \(f_0,\dots, f_{m-1}\) be homeomorphisms on a compact metric space \((X, d)\) to itself. Let \(h(f_0, f_1, \dots, f_{
Zhu, Li, Ma, Dongkui
exaly   +2 more sources

A Remark on Topological Sequence Entropy

International Journal of Bifurcation and Chaos, 2017
Let [Formula: see text] be the supremum of all topological sequence entropies of a dynamical system [Formula: see text]. This paper obtains the iteration invariance and commutativity of [Formula: see text] and proves that if [Formula: see text] is a multisensitive transformation defined on a locally connected space, then [Formula: see text].
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Metric Entropy and Topological Entropy

2012
This chapter is dedicated to the study of metric entropy, including its relation to topological entropy. After establishing some basic properties of metric entropy, we consider the notion of conditional entropy, and we show how generators can be used to compute metric entropy. We then establish the Shannon–McMillan–Breiman theorem, which can be seen as
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Topological Entropy for Geodesic Flows

The Annals of Mathematics, 1979
There have been many results in recent years showing that the topological entropy of a diffeomorphism [5], [16], [23], or a continuous map [11], [12], [17], is at least the logarithm of certain eigenvalues of the map it induces in real homology. These relationships, conjectured by Shub [21, p.
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Crisis and topological entropy

Physical Review E, 1995
, Fan, , Chay
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Topological Sequence Entropy

Proceedings of the London Mathematical Society, 1974
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