PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

A combinatorial invariant for escape time Sierpiński rational maps

Volume 222 / 2013

Mónica Moreno Rocha Fundamenta Mathematicae 222 (2013), 99-130 MSC: Primary 37F10; Secondary 37F20. DOI: 10.4064/fm222-2-1

Abstract

An escape time Sierpiński map is a rational map drawn from the McMullen family $z \mapsto z^n+\lambda /z^n$ with escaping critical orbits and Julia set homeomorphic to the Sierpiński curve continuum.

We address the problem of characterizing postcritically finite escape time Sierpiński maps in a combinatorial way. To accomplish this, we define a combinatorial model given by a planar tree whose vertices come with a pair of combinatorial data that encodes the dynamics of critical orbits. We show that each escape time Sierpiński map realizes a subgraph of the combinatorial tree and the combinatorial information is a complete conjugacy invariant.

Authors

  • Mónica Moreno RochaCentro de Investigación en Matemáticas, A.C.
    36240 Guanajuato, México
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image