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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:
37E45 Rotation numbers and vectors
37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
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