Topological Entropy of a Continuous Family of Smooth Time-Varying Dynamical Systems on an Interval Does Not Belong to the Second Baire Class

2020 ◽  
Vol 56 (1) ◽  
pp. 131-134
Author(s):  
A. N. Vetokhin
Keyword(s):  
Dynamical Systems ◽  
Topological Entropy ◽  
Baire Class ◽  
Continuous Family ◽  
Time Varying

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.

A Wavelet Based Procedure to Study Vibrations and Stability

1999 ◽  
Author(s):  
S. Pernot ◽  
C. H. Lamarque
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Periodic Solutions ◽  
Time Varying ◽  
Differential Systems ◽  
Varying Coefficients ◽  
Linear Differential Systems ◽  
Time Varying Coefficients ◽  
Linear Differential

Abstract A Wavelet-Galerkin procedure is introduced in order to obtain periodic solutions of multidegrees-of-freedom dynamical systems with periodic time-varying coefficients. The procedure is then used to study the vibrations of parametrically excited mechanical systems. As problems of stability analysis of nonlinear systems are often reduced after linearization to problems involving linear differential systems with time-varying coefficients, we demonstrate the method provides efficient practical computations of Floquet exponents and consequently allows to give estimators for stability/instability levels. A few academic examples illustrate the relevance of the method.

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