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Development of concept of topological entropy for systems with multiple time

Development of concept of topological entropy for systems with multiple time We study the topological entropy for dynamical systems with discrete or continuous multiple time. Due to the generalization of a well-known one time-dimensional result we show that the definition of topological entropy, using the approach for subshifts, leads to the zero entropy for many systems different from subshift. We define a new type of relative topological entropy to avoid this phenomenon. The generalization of Bowen’s power rule allows us to define topological and relative topological entropies for systems with continuous multiple time. As an application, we find a relation between the relative topological entropy and controllability of linear systems with continuous multiple time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Development of concept of topological entropy for systems with multiple time

Anikushin, M.; Reitmann, V.
Differential Equations , Volume 52 (13) – Mar 4, 2017
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References (33)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266116130012
Publisher site
See Article on Publisher Site

Abstract

We study the topological entropy for dynamical systems with discrete or continuous multiple time. Due to the generalization of a well-known one time-dimensional result we show that the definition of topological entropy, using the approach for subshifts, leads to the zero entropy for many systems different from subshift. We define a new type of relative topological entropy to avoid this phenomenon. The generalization of Bowen’s power rule allows us to define topological and relative topological entropies for systems with continuous multiple time. As an application, we find a relation between the relative topological entropy and controllability of linear systems with continuous multiple time.

Journal

Differential Equations – Springer Journals

Published: Mar 4, 2017

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