Bulletin of the Brazilian Mathematical Society

, Volume 37, Issue 2, pp 275–306

Pseudo-rotations of the open annulus


  • F. Béguin
    • Laboratoire de MathématiquesUniversité Paris Sud
  • S. Crovisier
    • CNRS—Laboratoire Analyse, Géométrie et ApplicationsUMR 7539, Institut Galilée, Université Paris
  • F. Le Roux
    • Laboratoire de MathématiquesUniversité Paris Sud

DOI: 10.1007/s00574-006-0013-2

Cite this article as:
Béguin, F., Crovisier, S. & Le Roux, F. Bull Braz Math Soc, New Series (2006) 37: 275. doi:10.1007/s00574-006-0013-2


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 Cr topology for any r ≥ 0.


rotation numberannulusPoincaré-Birkhoff

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© Springer-Verlag Berlin Heidelberg 2006