# Conjugacy between trapezoid maps

Volume 9, Issue 3, pp 819--826 Publication Date: March 25, 2016
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### Authors

Yong-Guo Shi - Key Laboratory of Numerical Simulation of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112, P. R. China.

### Abstract

Trapezoid maps are a kind of continuous and piecewise linear maps with a at top. By the conjugacy relationship, we present a complete classification for four families of trapezoid maps. Firstly, using an extension method, we construct all homeomorphic solutions of conjugacy equation $\varphi \circ f = g \circ \varphi$ for some non-monotone continuous maps f and g. Secondly, using an iterative construction method and an extension method, we construct respectively all topological conjugacies for four families of trapezoid maps. Finally, all construction algorithms are implemented in MATLAB, and three examples are illustrated to construct topological conjugacies and a topological semi-conjugacy.

### Keywords

• Trapezoid map
• topological conjugacy
• topological classification
• conjugacy equation.

•  37E05
•  37C15

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