%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 %0 Book %T Chaos: a mathematical introduction %A J. Banks %A V. Dragan %A A. Jones %D 2003 %I Cambridge University Press %C Cambridge %F Banks2003 %0 Journal Article %T Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval %A L. Block %A E. M. Coven %J Trans. Amer. Math. Soc. %D 1987 %V 300 %F Block1987 %0 Journal Article %T Monotonicity properties of the family of trapezoidal maps %A K. M. Brucks %A M. Misiurewicz %A C. Tresser %J Comm. Math. Phys. %D 1991 %V 137 %F Brucks1991 %0 Book %T Lectures on Ergodic Theory %A P. R. Halmos %D 1960 %I Chelsea Publishing Co. %C New York %F Halmos 1960 %0 Book %T Delta-pseudo orbit shadowing in a family of trapezoidal maps %A S. J. Kolodzieski %D 1991 %I Ph.D. Thesis, Stevens Institute of Technology, ProQuest LLC %C Ann Arbor, MI %F Kolodzieski 1991 %0 Book %T Symbolic dynamics of trapezoidal maps %A J. D. Louck %A N. Metropolis %D 1986 %I D. Reidel Publishing Co. %C Dordrecht %F Louck1986 %0 Journal Article %T On the existence of a conjugacy between weakly multimodal maps %A H. Segawa %A H. Ishitani %J Tokyo J. Math. %D 1998 %V 21 %F Segawa1998 %0 Journal Article %T Continuous functions that conjugate trapezoid functions %A B. Schweizer %A A. Sklar %J Aequationes Math. %D 1985 %V 28 %F Schweizer1985 %0 Journal Article %T Conjugacy and iterative roots of a class of piecewise expanding self-maps (I) %A G. Zhang %J (in Chinese), Chin. Ann. Math. %D 1992 %V 13 %F Zhang1992