Topological entropy dimension for nonautonomous dynamical systems

2019 ◽  
Vol 475 (2) ◽  
pp. 1978-1991
Author(s):  
Zhiqiang Li ◽  
Wenda Zhang ◽  
Wei Wang
Keyword(s):  
Dynamical Systems ◽  
Topological Entropy ◽  
Entropy Dimension ◽  
Nonautonomous Dynamical Systems

Remarks on Topological Entropy of Nonautonomous Dynamical Systems

2015 ◽  
Vol 25 (12) ◽  
pp. 1550158 ◽  
Author(s):  
Zhiming Li
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Topological Entropy ◽  
Nonautonomous Dynamical Systems ◽  
Nonautonomous Dynamical System

In this paper, we give several classical definitions of topological entropy (on a noncompact and noninvariant subset) for nonautonomous dynamical system. Furthermore, their relationships are established.

scholarly journals Topological entropy of nonautonomous dynamical systems

2020 ◽  
Vol 268 (9) ◽  
pp. 5353-5365
Author(s):  
Kairan Liu ◽  
Yixiao Qiao ◽  
Leiye Xu
Keyword(s):  
Dynamical Systems ◽  
Topological Entropy ◽  
Nonautonomous Dynamical Systems

On Generic Properties of Nonautonomous Dynamical Systems

2018 ◽  
Vol 28 (08) ◽  
pp. 1850102 ◽  
Author(s):  
Francisco Balibrea ◽  
Jaroslav Smítal ◽  
Marta Štefánková
Keyword(s):  
Dynamical Systems ◽  
Topological Entropy ◽  
Compact Space ◽  
Metric Space ◽  
Generic Properties ◽  
Compact Metric Space ◽  
Continuous Map ◽  
Nonautonomous Dynamical Systems ◽  
Uniformly Convergent ◽  
Generic System

We consider nonautonomous dynamical systems consisting of sequences of continuous surjective maps of a compact metric space [Formula: see text]. Let [Formula: see text], [Formula: see text] and [Formula: see text] denote the space of systems [Formula: see text], which are uniformly convergent, or equicontinuous, or pointwise convergent (to a continuous map), respectively. We show that for [Formula: see text], the generic system in any of the spaces has infinite topological entropy, while, if [Formula: see text] is the Cantor set, the generic system in any of the spaces has zero topological entropy. This shows, among others, that the general results of the above type for arbitrary compact space [Formula: see text] are difficult if not impossible.

scholarly journals On some kinds of dense orbits in general nonautonomous dynamical systems

2020 ◽  
Vol 7 (1) ◽  
pp. 163-175
Author(s):  
Mehdi Pourbarat
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Point Of View ◽  
Topological Conjugacy ◽  
Topological Transitivity ◽  
Nonautonomous Systems ◽  
Nonautonomous Dynamical Systems ◽  
Sensitive Dependence ◽  
Dense Orbits

AbstractWe study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.

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.

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