A combinatorial invariant for escape time Sierpiński rational maps
Tom 222 / 2013
Fundamenta Mathematicae 222 (2013), 99-130
MSC: Primary 37F10; Secondary 37F20.
DOI: 10.4064/fm222-2-1
Streszczenie
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.
