Results 301 to 310 of about 740,617 (344)

Worst-case topological entropy and minimal data rate for state observation of switched linear systems

International Conference on Hybrid Systems: Computation and Control, 2020
We introduce and study the concept of worst-case topological entropy of switched linear systems under arbitrary switching. It is shown that this quantity is equal to the minimal data rate (number of bits per second) required for the state observation of ...
Guillaume O. Berger, R. Jungers
semanticscholar   +1 more source

The topological Rohlin property and topological entropy [PDF]

American Journal of Mathematics, 2001
For a compact metric space X let G = H ( X ) denote the group of self homeomorphisms with the topology of uniform convergence. The group G acts on itself by conjugation and we say that X satisfies the topological Rohlin property if this action has dense orbits.
Eli Glasner, Benjamin Weiss
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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 ...
Stewart Baldwin, Edward E. Slaminka
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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.
Gabriel P. Paternain, Miguel Paternain
openaire   +3 more sources

On Topological Entropy of Switched Linear Systems with Diagonal, Triangular, and General Matrices

IEEE Conference on Decision and Control, 2018
This paper introduces a notion of topological entropy for switched systems, formulated using the minimal number of initial states needed to approximate all initial states within a finite precision.
Guosong Yang, A. J. Schmidt, D. Liberzon
semanticscholar   +1 more source

Lowering topological entropy

Journal d'Analyse Mathématique, 1995
The author considers the topological entropy of (topological) factors of a given dynamical system \((X, T)\) with positive entropy \(h\). He shows that if \(X\) is a finite-dimensional space (i.e. a space of finite topological dimension), then there exist factors with all values of entropy between 0 and \(h\).
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On topological entropy of maps

Ergodic Theory and Dynamical Systems, 1995
AbstractWe introduce an ‘entropy’ hm(f) for a continuous mapping of a compact metric space to itself which is denned in terms of (n, ∈)-separated subsets of inverse images of individual points. This invariant is compared with the inverse-image entropy h_(f) introduced recently by Langevin and Walczak. The two main results are: (1) the inequality hm(f) ≤
openaire   +3 more sources

Metric Entropy and Topological Entropy [PDF]

, 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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Physical Analysis of Heat of Formation and Entropy for Ceria Oxide Using Topological Indices.

Combinatorial chemistry & high throughput screening, 2020
BACKGROUND "Cerium oxide nanoparticles (.
Xiujun Zhang, M. K. Siddiqui, Sana Javed, L. Sherin, Farah Kausar, Mehwish Hussain Muhammad   +5 more
semanticscholar   +1 more source

Topological R-entropy and topological entropy of free semigroup actions

Journal of Mathematical Analysis and Applications, 2019
Abstract We introduce the notion of topological r-entropy for free semigroup actions on a compact metric space and provide some properties of it. By using the skew-product transformation as bridge, we get the following two main results. 1. We extend the result that the topological entropy is the limit of topological r-entropy in [15] to free ...
Li Zhu, Dongkui Ma
openaire   +2 more sources