Family of Dynamical Systems Whose Topological Entropy Is Nowhere Upper Semicontinuous

2019 ◽  
Vol 55 (8) ◽  
pp. 1118-1119
Author(s):  
A. N. Vetokhin
Keyword(s):  
Dynamical Systems ◽  
Topological Entropy ◽  
Upper Semicontinuous

scholarly journals On the Relation between Topological Entropy and Restoration Entropy

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 7 ◽  
Author(s):  
Christoph Kawan
Keyword(s):  
Dynamical Systems ◽  
State Estimation ◽  
Topological Entropy ◽  
Robust Estimation ◽  
Data Transmission ◽  
Communication Constraints ◽  
Dynamical Entropy

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.

scholarly journals Topological Entropy of One Type of Nonoriented Lorenz-Type Maps

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Guo Feng
Keyword(s):  
Dynamical Systems ◽  
Topological Entropy ◽  
Poincaré Map ◽  
Geometric Model ◽  
Dynamical Property ◽  
High Dimensional ◽  
Poincare Map ◽  
One Dimensional

Constructing a Poincaré map is a method that is often used to study high-dimensional dynamical systems. In this paper, a geometric model of nonoriented Lorenz-type attractor is studied using this method, and its dynamical property is described. The topological entropy of one-dimensional nonoriented Lorenz-type maps is also computed in terms of their kneading sequences.

scholarly journals A Dynamical Systems-Based Hierarchy for Shannon, Metric and Topological Entropy

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 938
Author(s):  
Raymond Addabbo ◽  
Denis Blackmore
Keyword(s):  
Dynamical Systems ◽  
Topological Entropy ◽  
Shannon Entropy ◽  
Shannon Information ◽  
Metric Entropy ◽  
Special Case

A rigorous dynamical systems-based hierarchy is established for the definitions of entropy of Shannon (information), Kolmogorov–Sinai (metric) and Adler, Konheim & McAndrew (topological). In particular, metric entropy, with the imposition of some additional properties, is proven to be a special case of topological entropy and Shannon entropy is shown to be a particular form of metric entropy. This is the first of two papers aimed at establishing a dynamically grounded hierarchy comprising Clausius, Boltzmann, Gibbs, Shannon, metric and topological entropy in which each element is ideally a special case of its successor or some kind of limit thereof.

Sign in / Sign up

Export Citation Format

Share Document