Abstract

The Chebyshev map is a typical chaotic map. Fbw things are known about the dynamics of generalized Chebyshev maps in higher dimensions. Generalized Chebyshev maps are related to the theory of complex Lie algebras and affie Weyl groups. In a former note we showed that bivariate Chebyshev maps of $\mathrm{C}^{2} $ are also chaotic and the support of the maximal entropy measure $\mu $ of each Chebyshev map is connected. In this note, we perturb a bivariate Chebyshev map in a certain direction. Then, we show that the support $\mu $ of a perturbed map is a Cantor sets. 1