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

• Autorzy: Huaibin Li , Weixiao Shen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37F35: Conformal densities and Hausdorff dimension

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 198
• Numer: 2
• Strony: 165-176

Daty

wydano

2008

Twórcy

autor

Huaibin Li

• Mathematics Department, University of Science and Technology of China, Hefei 230026, China

autor

Weixiao Shen

• Mathematics Department, University of Science and Technology of China, Hefei 230026, China

Identyfikatory

DOI

10.4064/fm198-2-6