Parabolic orbifolds and the dimension of the maximal measure for rational maps.

Anna Zdunik

Displaying similar documents to “Parabolic orbifolds and the dimension of the maximal measure for rational maps.”

One-sided Lebesgue Bernoulli maps of the sphere of degree $n^{2}$ and $2 n^{2}$ .

Barnes, Julia A., Koss, Lorelei (2000)

International Journal of Mathematics and Mathematical Sciences

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Dimensions of the Julia sets of rational maps with the backward contraction property

Huaibin Li, Weixiao Shen (2008)

Fundamenta Mathematicae

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Consider a rational map f on the Riemann sphere of degree at least 2 which has no parabolic periodic points. Assuming that f has Rivera-Letelier's backward contraction property with an arbitrarily large constant, we show that the upper box dimension of the Julia set J(f) is equal to its hyperbolic dimension, by investigating the properties of conformal measures on the Julia set.