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Non-autonomous systems on Lie groups and their topological entropy

Abstract

In the present paper we introduce and study the topological entropy of non-autonomous dynamical systems and define the non-autonomous dynamical system on Lie groups and manifolds. Our main purpose is to estimate the topological entropy of the non-autonomous dynamical system on Lie groups. We show that the topological entropy of the non-autonomous dynamical system on Lie groups and induced Lie algebra are equal under topological conjugacy, and a method to estimate the topological entropy of non-autonomous systems on Lie groups is given. To illustrate our results, some examples are presented. Finally some discussions and comments about positive entropy on nil-manifold Lie groups for non-autonomous systems are presented.

Key words: Lie group, topological entropy, non-autonomous, exponential map, Lie algebra, conjugacy.

Article Information

 Title Non-autonomous systems on Lie groups and their topological entropy Source Methods Funct. Anal. Topology, Vol. 25 (2019), no. 4, 360-372 MathSciNet MR4049690 Milestones Received 05/02/2019; Revised 12/10/2019 Copyright The Author(s) 2019 (CC BY-SA)

Authors Information

M. Fatehi Nia
Department of Mathematics, Yazd University, Yazd, Iran

Department of Mathematics, Yazd University, Yazd, Iran

Citation Example

M. Fatehi Nia and F. Moeinaddini, Non-autonomous systems on Lie groups and their topological entropy, Methods Funct. Anal. Topology 25 (2019), no. 4, 360-372.

BibTex

@article {MFAT1243,
AUTHOR = {M. Fatehi Nia and F. Moeinaddini},
TITLE = {Non-autonomous systems on Lie groups and their topological entropy},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {4},
PAGES = {360-372},
ISSN = {1029-3531},
MRNUMBER = {MR4049690},
URL = {http://mfat.imath.kiev.ua/article/?id=1243},
}

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