Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts

Details Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts

2007-11-16

arxiv.org/abs/0711.2672v1

Internat. Math. Res. Notices 2009 (2009), 615-624

Mathematics

Dynamical Systems

7 pages, 1 figure

Scientific paper

10.1093/imrn/rnn141

We prove that for meromorphic maps with logarithmic tracts (e.g. entire or
meromorphic maps with a finite number of poles from class $\mathcal B$), the
Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff
dimension greater than 1. Hence, the hyperbolic dimension of the Julia set is
greater than 1.

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