Topological Conjugacy Between Skew Tent Maps

Abstract

This paper investigates the conjugacy of any two skew tent maps. An explicit formula is given for the conjugacy. It is proved that the conjugacy is singular, Hölder continuous and not differentiable as well as its inverse. We calculate the arc-length of the conjugacy curve and the area under the conjugacy curve. We construct a sequence of functions to approximate the conjugacy, and give an estimation for the error of the approximation.