Conjugacy between trapezoid maps
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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.
Share and Cite
ISRP Style
Yong-Guo Shi, Conjugacy between trapezoid maps, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 819--826
AMA Style
Shi Yong-Guo, Conjugacy between trapezoid maps. J. Nonlinear Sci. Appl. (2016); 9(3):819--826
Chicago/Turabian Style
Shi, Yong-Guo. "Conjugacy between trapezoid maps." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 819--826
Keywords
- Trapezoid map
- topological conjugacy
- topological classification
- conjugacy equation.
MSC
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