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Université d'Angers - L003
On combInaTorIal types of Cycles under $z^d$
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 $0< x_1 < x_2 < \ldots x_q <1\in\TT := \RR/\ZZ$ fixing $0\equiv 1$ 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 $d$?