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An escape time Sierpiński map is a rational map drawn from the McMullen family z ↦ zⁿ + λ/zⁿ 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.
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
99-130
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
- Centro de Investigación en Matemáticas, A.C., 36240 Guanajuato, México
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-2-1