A combinatorial invariant for escape time Sierpiński rational maps

• Autorzy: Mónica Moreno Rocha
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37F20: Combinatorics and topology
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 222
• Numer: 2
• Strony: 99-130

Daty

wydano

2013

Twórcy

autor

Mónica Moreno Rocha

• Centro de Investigación en Matemáticas, A.C., 36240 Guanajuato, México

Identyfikatory

DOI

10.4064/fm222-2-1