caa a22 4500 445836067 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0657-x doi (NATIONALLICENCE)springer-10.1007/s00209-009-0657-x Homeomorphisms of the annulus with a transitive lift [Elektronische Daten] [Salvador Addas-Zanata, Fábio Tal] Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift $${\tilde{f}}$$ to the infinite strip à which is transitive. We show that, if the rotation numbers of both boundary components of A are strictly positive, then there exists a closed nonempty unbounded set $${B^{-} \subset \tilde{A}}$$ such that B − is bounded to the right, the projection of B − to A is dense, $${B^{-}-(1, 0) \subset B^{-}}$$ and $${\tilde{f}(B^{-}) \subset B^{-}}$$. Moreover, if p 1 is the projection on the first coordinate of Ã, then there exists d>0 such that, for any $${\tilde z \in B^{-}}$$, $$\limsup_{n\to\infty}\frac{p_1(\tilde f^n(\tilde z))-p_1(\tilde z)}{n}<-d.$$ 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. Springer-Verlag, 2009 Closed connected sets nationallicence Transitivity nationallicence Periodic orbits nationallicence Compactification nationallicence Addas-Zanata Salvador Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil aut Tal Fábio Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil aut Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 971-980 0025-5874 267:3-4<971 2011 267 209 https://doi.org/10.1007/s00209-009-0657-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0657-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Addas-Zanata Salvador Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil aut NATIONALLICENCE 700 1- Tal Fábio Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 971-980 0025-5874 267:3-4<971 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer