Pseudo-rotations of the open annulus

Béguin, F.; Crovisier, S.; Roux, F. Le

Pseudo-rotations of the open annulus

Authors

Béguin, F.

Crovisier, S.

Roux, F. Le

Description

In this paper, we study pseudo-rotations of the open annulus, \emph{i.e.} conservative homeomorphisms of the open annulus whose rotation set is reduced to a single irrational number (the angle of the pseudo-rotation). We prove in particular that, for every pseudo-rotation $h$ of angle $ρ$, the rigid rotation of angle $ρ$ is in the closure of the conjugacy class of $h$. We also prove that pseudo-rotations are not persistent in $C^r$ topology for any $r\geq 0$.
25 pages