TY - JOUR AU - Shi, Yong-Guo PY - 2016 TI - Conjugacy between trapezoid maps JO - Journal of Nonlinear Sciences and Applications SP - 819--826 VL - 9 IS - 3 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.03.10 DO - 10.22436/jnsa.009.03.10 ID - Shi2016 ER - TY - BOOK TI - Chaos: a mathematical introduction AU - J. Banks AU - V. Dragan AU - A. Jones PB - Cambridge University Press PY - 2003 DA - 2003// CY - Cambridge ID - Banks2003 ER - TY - JOUR TI - Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval AU - L. Block AU - E. M. Coven JO - Trans. Amer. Math. Soc. PY - 1987 DA - 1987// VL - 300 ID - Block1987 ER - TY - JOUR TI - Monotonicity properties of the family of trapezoidal maps AU - K. M. Brucks AU - M. Misiurewicz AU - C. Tresser JO - Comm. Math. Phys. PY - 1991 DA - 1991// VL - 137 ID - Brucks1991 ER - TY - BOOK TI - Lectures on Ergodic Theory AU - P. R. Halmos PB - Chelsea Publishing Co. PY - 1960 DA - 1960// CY - New York ID - Halmos 1960 ER - TY - BOOK TI - Delta-pseudo orbit shadowing in a family of trapezoidal maps AU - S. J. Kolodzieski PB - Ph.D. Thesis, Stevens Institute of Technology, ProQuest LLC PY - 1991 DA - 1991// CY - Ann Arbor, MI ID - Kolodzieski 1991 ER - TY - BOOK TI - Symbolic dynamics of trapezoidal maps AU - J. D. Louck AU - N. Metropolis PB - D. Reidel Publishing Co. PY - 1986 DA - 1986// CY - Dordrecht ID - Louck1986 ER - TY - JOUR TI - On the existence of a conjugacy between weakly multimodal maps AU - H. Segawa AU - H. Ishitani JO - Tokyo J. Math. PY - 1998 DA - 1998// VL - 21 ID - Segawa1998 ER - TY - JOUR TI - Continuous functions that conjugate trapezoid functions AU - B. Schweizer AU - A. Sklar JO - Aequationes Math. PY - 1985 DA - 1985// VL - 28 ID - Schweizer1985 ER - TY - JOUR TI - Conjugacy and iterative roots of a class of piecewise expanding self-maps (I) AU - G. Zhang JO - (in Chinese), Chin. Ann. Math. PY - 1992 DA - 1992// VL - 13 ID - Zhang1992 ER -