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Seminário de Sistemas Dinâmicos - "On Combinatorial Types of Cycles under $z^d$"
Terça-feira 03 Julho 2018, 16:00 - 18:00
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Seminário de Sistemas Dinâmicos

Título: On Combinatorial Types of Cycles under $z^d$

Palestrante: Carsten Lunde Petersen (Roskilde University)

Resumo: The talk is based on joint work with Saeed Zakeri. Rotation sets for $z^d$, sets on which $z^d$ is topologically conjugate to a rigid rotation, are well studied in the literature. Much less is known about periodic orbits of other types of combinatorics. To be precise by a combinatorics (of period $q$) we mean a dynamics on $0< x_1 < x_2 < ldots x_q <1inTT := RR/ZZ$ fixing $0equiv 1$ and which acts as a permutation of order $q$ on the $x_i$. Which combinatorics are realized under $z^d$? In how many distinct ways is a given combinatorics realized? How does this number depend on the degree $d$? We give complete answers to these questions in simple terms. The answers generalize works of Bullet and Sentenac for degree $2$ and of McMullen.

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