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Pseudo-rotations of the open annulus. (English) Zbl 1105.37029
Summary: We study pseudo-rotations of the open annulus, 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 $$\rho$$, the rigid rotation of angle $$\rho$$ 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 $$r \geq 0$$.

##### MSC:
 3.7e+46 Rotation numbers and vectors 3.7e+31 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
##### Keywords:
rotation number; annulus; Poincaré-Birkhoff
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