# Complex dynamics and quasi-conformal geometry.

Oct 23 – 25, 2017
Université d'Angers
Europe/Paris timezone

## On combInaTorIal types of Cycles under $z^d$

Oct 25, 2017, 9:00 AM
55m
L003 (Université d'Angers)

### L003

#### Université d'Angers

2 Boulevard Lavoisier 49000 Angers

### Speaker

Carsten Lunde Petersen (INM at Roskilde University)

### Description

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 $d$?

### Primary author

Carsten Lunde Petersen (INM at Roskilde University)

### Presentation materials

 Transparents