Generalized Chebyshev maps of $\mathbf{C}^{2}$ and their perturbations
Uchimura, Keisuke
Osaka J. Math., Tome 46 (2009) no. 1, p. 995-1017 / Harvested from Project Euclid
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The Chebyshev map is a typical chaotic map. We consider generalized Chebyshev maps $T_{k}$ of $\mathbf{C}^{2}$. The support of the maximal entropy measure of $T_{k}$ is connected. We perturb $T_{k}$ in a certain direction. Then we can show the support of the maximal entropy measure of this map is a Cantor set.
Publié le : 2009-12-15
Classification:  32H50,  37F45,  37F10 
@article{1260892837,
     author = {Uchimura, Keisuke},
     title = {Generalized Chebyshev maps of $\mathbf{C}^{2}$ and their perturbations},
     journal = {Osaka J. Math.},
     volume = {46},
     number = {1},
     year = {2009},
     pages = { 995-1017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1260892837}
}

Uchimura, Keisuke. Generalized Chebyshev maps of $\mathbf{C}^{2}$ and their perturbations. Osaka J. Math., Tome 46 (2009) no. 1, pp.  995-1017. http://gdmltest.u-ga.fr/item/1260892837/