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Subjects
37-XX Dynamical systems and ergodic theory
37Fxx Complex dynamical systems
37F20 Combinatorics and topology

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On a theorem of Rees-Shishikura

Guizhen Cui, Wenjuan Peng, Lei Tan (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Rees-Shishikura’s theorem plays an important role in the study of matings of polynomials. It promotes Thurston’s combinatorial equivalence into a semi-conjugacy. In this work we restate and reprove Rees-Shishikura’s theorem in a more general form, which can then be applied to a wider class of postcritically finite branched coverings. We provide an application of the restated theorem.

On supports of dynamical laminations and biaccessible points in polynomial Julia sets

Stanislav K. Smirnov (2001)

Colloquium Mathematicae

We use Beurling estimates and Zdunik's theorem to prove that the support of a lamination of the circle corresponding to a connected polynomial Julia set has zero length, unless f is conjugate to a Chebyshev polynomial. Equivalently, except for the Chebyshev case, the biaccessible points in the connected polynomial Julia set have zero harmonic measure.

Currently displaying 1 – 2 of 2

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