Chaos in a topologically transitive semi-flow

Volume 10, Issue 4, pp 1675--1682 http://dx.doi.org/10.22436/jnsa.010.04.30

Publication Date: April 20, 2017 Submission Date: October 27, 2016

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Authors

Risong Li - School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, P. R. China. Tianxiu Lu - Department of Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, P. R. China.

Abstract

In this paper, we study the chaotic phenomena in a topologically transitive, continuous semi-flow, and show that the erratic time dependence of orbits in such a semi-flow is more complicated than the one described by Li-Yorke chaos. Also, we generalize the notion of sensitive dependence on initial conditions for semi-flows and explore the chaotic phenomena for topologically transitive, continuous semi-flows with the generalized sensitivity property. Our results extend the existing results to semi-flows.

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Keywords

• Chaos
• topological transitivity
• sensitive dependence.

MSC

•  54H20
•  37A05
•  28D05
•  37A25

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