Bulletin of the Brazilian Mathematical Society

, Volume 37, Issue 2, pp 275-306

Pseudo-rotations of the open annulus

  • F. BéguinAffiliated withLaboratoire de Mathématiques, Université Paris Sud
  • , S. CrovisierAffiliated withCNRS—Laboratoire Analyse, Géométrie et Applications, UMR 7539, Institut Galilée, Université Paris
  • , F. Le RouxAffiliated withLaboratoire de Mathématiques, Université Paris Sud

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In this paper, 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 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 ≥ 0.


rotation number annulus Poincaré-Birkhoff

Mathematical subject classification:

37E45 37E30