%0 Journal Article %T Conjugacy between trapezoid maps %A Shi, Yong-Guo %J Journal of Nonlinear Sciences and Applications %D 2016 %V 9 %N 3 %@ ISSN 2008-1901 %F Shi2016 %X 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. %9 journal article %R 10.22436/jnsa.009.03.10 %U http://dx.doi.org/10.22436/jnsa.009.03.10 %P 819--826