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Pseudo-rotations of the open annulus

F. Béguin·S. Crovisier·F. Le Roux
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Abstract

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 $r\geq 0$.

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F. Béguin, S. Crovisier, F. Le Roux. 2005-06-02. Pseudo-rotations of the open annulus. https://arxiv.org/abs/math/0506041

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