Geodesic
Dimensions of the Julia sets of rational maps with the backward contraction property
Huaibin Li 1   ; Weixiao Shen 1
1 Mathematics Department University of Science and Technology of China Hefei 230026, China
Fundamenta Mathematicae, Tome 198 (2008) no. 2, pp. 165-176 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm198-2-6
Keywords: consider rational map riemann sphere degree least which has parabolic periodic points assuming has rivera leteliers backward contraction property arbitrarily large constant upper box dimension julia set equal its hyperbolic dimension investigating properties conformal measures julia set

Huaibin Li  1   ; Weixiao Shen  1

1 Mathematics Department University of Science and Technology of China Hefei 230026, China 
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Huaibin Li; Weixiao Shen. Dimensions of the Julia sets of rational maps
 with the backward contraction property. Fundamenta Mathematicae, Tome 198 (2008) no. 2, pp. 165-176. doi: 10.4064/fm198-2-6

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