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Entropy 2018, 20(2), 128; https://doi.org/10.3390/e20020128

On Points Focusing Entropy

Faculty of Mathematics and Computer Science, ódź University, Banacha 22, 90-238 ódź, Poland
These authors contributed equally to this work.
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Received: 22 January 2018 / Revised: 12 February 2018 / Accepted: 13 February 2018 / Published: 16 February 2018
(This article belongs to the Special Issue Entropy in Dynamic Systems)
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Abstract

In the paper, we consider local aspects of the entropy of nonautonomous dynamical systems. For this purpose, we introduce the notion of a (asymptotical) focal entropy point. The notion of entropy appeared as a result of practical needs concerning thermodynamics and the problem of information flow, and it is connected with the complexity of a system. The definition adopted in the paper specifies the notions that express the complexity of a system around certain points (the complexity of the system is the same as its complexity around these points), and moreover, the complexity of a system around such points does not depend on the behavior of the system in other parts of its domain. Any periodic system “acting” in the closed unit interval has an asymptotical focal entropy point, which justifies wide interest in these issues. In the paper, we examine the problems of the distortions of a system and the approximation of an autonomous system by a nonautonomous one, in the context of having a (asymptotical) focal entropy point. It is shown that even a slight modification of a system may lead to the arising of the respective focal entropy points. View Full-Text
Keywords: nonautonomous (autonomous) dynamical system; topological entropy; (asymptotical) focal entropy point; disturbation; m-dimensional manifold nonautonomous (autonomous) dynamical system; topological entropy; (asymptotical) focal entropy point; disturbation; m-dimensional manifold
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Korczak-Kubiak, E.; Loranty, A.; Pawlak, R.J. On Points Focusing Entropy. Entropy 2018, 20, 128.

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