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- W2950311320 abstract "Let $f:hat{C}tohat{C}$ be a subhyperbolic rational map of degree $d$. We construct a set of coding maps $Cod(f)={pi_r:Sigmato J}_r$ of the Julia set $J$ by geometric coding trees, where the parameter $r$ ranges over mappings from a certain tree to the Riemann sphere. Using the universal covering space $phi:tilde Sto S$ for the corresponding orbifold, we lift the inverse of $f$ to an iterated function system $I=(g_i)_{i=1,2,...,d}$. For the purpose of studying the structure of $Cod(f)$, we generalize Kenyon and Lagarias-Wang's results : If the attractor $K$ of $I$ has positive measure, then $K$ tiles $phi^{-1}(J)$, and the multiplicity of $pi_r$ is well-defined. Moreover, we see that the equivalence relation induced by $pi_r$ is described by a finite directed graph, and give a necessary and sufficient condition for two coding maps $pi_r$ and $pi_{r'}$ to be equal." @default.
- W2950311320 created "2019-06-27" @default.
- W2950311320 creator A5025553017 @default.
- W2950311320 date "2003-06-25" @default.
- W2950311320 modified "2023-09-27" @default.
- W2950311320 title "Coding and tiling of Julia sets for subhyperbolic rational maps" @default.
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