On generic rotationless diffeomorphisms of the annulus

Addas-Zanata, Salvador; Tal, Fábio

doi:10.1090/S0002-9939-09-10135-1

On generic rotationless diffeomorphisms of the annulus
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by Salvador Addas-Zanata and Fábio Armando Tal PDF

Proc. Amer. Math. Soc. 138 (2010), 1023-1031 Request permission

Abstract:

Let $f$ be a $C^r$-diffeomorphism of the closed annulus $A$ that preserves the orientation, the boundary components and the Lebesgue measure. Suppose that $f$ has a lift $\tilde f$ to the infinite strip $\tilde A$ which has zero Lebesgue measure rotation number. If the rotation number of $\tilde f$ restricted to both boundary components of $A$ is positive, then for such a generic $f$ ($r\geq 16$), zero is an interior point of its rotation set. This is a partial solution to a conjecture of P. Boyland.

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