Relationship between Li-Yorke chaos and positive topological sequence entropy in nonautonomous dynamical systems

Jakub Šotola

doi:10.3934/dcds.2018225

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2018, Volume 38, Issue 10: 5119-5128. Doi: 10.3934/dcds.2018225

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Relationship between Li-Yorke chaos and positive topological sequence entropy in nonautonomous dynamical systems

Jakub Šotola

Mathematical Institute, Silesian University in Opava, Na Rybníčku 626/1, Opava, 746 01, Czech Republic

Received: November 30, 2017

Revised: May 31, 2018

Published: September 2018

The author is supported by the grant SGS/18/2016.

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Abstract

We study chaotic properties of uniformly convergent nonautonomous dynamical systems. We show that, contrary to the autonomous systems on the compact interval, positivity of topological sequence entropy and occurrence of Li-Yorke chaos are not equivalent, more precisely, neither of the two possible implications is true.

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Mathematics Subject Classification: Primary: 54H20, 37B40, 37B55; Secondary: 37B10.

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Figure 1. Sketches of maps from proof of Lemma 3.1

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Figure 2. Sketches of limit map f and its perturbation, dotted lines are unspecified parts of the graph

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