2008/11/18 by Salvador Addas Zanata, Fábio Armando Tal, Zanata, Salvador Addas +2
Engineering · Mathematics · #Mathematics and Applications #Tribology and Lubrication Engineering #math.DS
paper · pdf · doi:10.48550/arxiv.0811.3003
arxiv created 2008/11/18 · arxiv updated 2009/12/01
Let f be a homeomorphism of the closed annulus A that preserves orientation, boundary components and that has a lift f to the infinite strip A which is transitive. We show that, if the rotation number of both boundary components of A is strictly positive, then there exists a closed nonempty connected set Γ⊂ A such that Γ⊂]-∞,0]×[0,1], Γ is unlimited, the projection of Γ to A is dense, Γ-(1,0)⊂Γ and f(Γ)⊂ Γ. Also, if p1 is the projection in the first coordinate in A, then there exists d>0 such that, for any z∈Γ, \limsupn→∞(p1( fn( z))-p1( z))/(n)<-d. In particular, using a result of Franks, we show that the rotation set of any homeomorphism of the annulus that preserves orientation, boundary components, which has a transitive lift without fixed points in the boundary is an interval with 0 in its interior.