On generic rotationless diffeomorphisms of the annulus

Abstract

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