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

Volume 198 / 2008

Huaibin Li, Weixiao Shen Fundamenta Mathematicae 198 (2008), 165-176 MSC: Primary 37F35. DOI: 10.4064/fm198-2-6

Abstract

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.

Authors

  • Huaibin LiMathematics Department
    University of Science and Technology of China
    Hefei 230026, China
    e-mail
  • Weixiao ShenMathematics Department
    University of Science and Technology of China
    Hefei 230026, China
    e-mail

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