Topological conjugacy of PM functions with height equaling \(\infty\)

Volume 10, Issue 11, pp 6062--6070 http://dx.doi.org/10.22436/jnsa.010.11.41

Publication Date: November 27, 2017 Submission Date: December 21, 2016

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Authors

Pingping Zhang - Department of Mathematics, Binzhou University, Shandong 256603, P. R. China.

Abstract

It is known that topological conjugacy is a basic equivalence relation in dynamical systems. In this paper we study a class of piecewise monotone and continuous functions with infinite height. Those functions are topologically conjugate with each other if and only if they have same sequences describing itineraries of all forts, endpoints, and fixed points. We construct the topological conjugacy by extension, which partly generalizes previous results.

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Keywords

• Topological conjugacy
• homeomorphism
• piecewise monotone
• fort

MSC

•  39B22
•  37C15
•  37E05
•  26A18

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