Conjugacy between trapezoid maps
نویسندگان
چکیده
Trapezoid maps are a kind of continuous and piecewise linear maps with a flat 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 φ ◦ f = g ◦ φ 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. c ©2016 All rights reserved.
منابع مشابه
On Rigidity of One-Dimensional Maps
The regularity of the conjugacy between two onedimensional maps with singular points is considered. We prove that the conjugacy between two nice and mixing quasi-hyperbolic one-dimensional maps is a diffeomorphism if it is an absolutely continuous homeomorphism and the exponents and the asymmetries of these two maps at all corresponding singular points are the same. We also discuss the applicat...
متن کاملThe geometry of some natural conjugacies in ℂn dynamics
We show that under some simple conditions a topological conjugacy h between two holomorphic self-maps f1 and f2 of complexn-dimensional projective space Pn lifts canonically to a topological conjugacy H between the two corresponding polynomial self-maps of Cn+1, and this conjugacy relates the two Green functions of f1 and f2. These conjugacies are interesting because their geometry is not inher...
متن کاملOn fuzzifications of discrete dynamical systems
Let X denote a locally compact metric space and φ : X → X be a continuous map. In the 1970s L. Zadeh presented an extension principle, helping us to fuzzify the dynamical system (X, φ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, Chaos, entropy and a generalized extension principle, Fuzzy Sets and Systems 61 (1994)] and we...
متن کاملNonlinearity, Quasisymmetry, Differentiability, And Rigidity in One-Dimensional Dynamics
In this article, we review some of our research in the study of one-dimensional dynamical systems, in particular, some technique and results in the study of the smooth classification of certain one-dimensional maps. The main results which we review are that if the conjugacy between two mixing and nice quasihyperbolic maps is differentiable at one point with uniform bound, then it is piecewise s...
متن کاملSuperconvergence of period doubling cascade in trapezoid maps Its Rigorous proof and superconvergence of period doubling cascade starting from a period p solution
In the symmetric and the asymmetric trapezoid maps, as a slope a of the trapezoid is increased, the period doubling cascade occurs and the symbolic sequence of periodic points is the Metropolis-Stein-Stein sequence R∗m and the convergence of the onset point am of the period 2 m solution to the accumulation point ac is exponentially fast. In the previous paper, we proved these results. In this p...
متن کامل