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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.

Information

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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