Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz

Abstract : Consider a homeomorphism h of the closed annulusS^1*[0,1], isotopic to the identity, such that therotation set of h is reduced to a single irrationalnumber alpha (we say that h is an irrationalpseudo-rotation).For every positive integer n, we prove that thereexists a simple arc gamma joining one of theboundary component of the annulus to the otherone, such that gamma is disjoint from its nfirst iterates under h. As a corollary, we obtain thatthe rigid rotation of angle alpha can beapproximated by homeomorphisms conjugate to h.The first result stated above is an analog of atheorem of J.\,Kwapisz dealing with diffeomorphisms of the two-torus; we give some new, purely two-dimensional, proofs,that work both for the annulus and for the toruscase.
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Submitted on : Monday, September 29, 2003 - 6:12:42 PM
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Sylvain Crovisier, Francois Beguin, Frederic Le Roux, Alice Patou. Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz. 2003. ⟨hal-00000654⟩

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