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Rotation sets with non-empty interior and transitivity in the universal covering

Published online by Cambridge University Press:  28 August 2013

NANCY GUELMAN ,
ANDRES KOROPECKI  and
FABIO ARMANDO TAL
NANCY GUELMAN
Affiliation:
IMERL, Facultad de Ingeniería, Universidad de la República, C.C. 30, Montevideo, Uruguay email nguelman@fing.edu.uy
ANDRES KOROPECKI
Affiliation:
Universidade Federal Fluminense, Instituto de Matemática e Estatística, Rua Mário Santos Braga S/N, 24020-140 Niteroi, RJ, Brasil email ak@id.uff.br
FABIO ARMANDO TAL
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo, SP, Brasil email fabiotal@ime.usp.br
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Abstract

Let $f$ be a transitive homeomorphism of the two-dimensional torus in the homotopy class of the identity. We show that a lift of $f$ to the universal covering is transitive if and only if the rotation set of the lift contains the origin in its interior.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 3 , May 2015 , pp. 883 - 894
Copyright
© Cambridge University Press, 2013 

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