Ergodicity and Annular Homeomorphisms of the Torus

Renato B. Bortolatto ^[1] ; Fabio A. Tal
1. [1] Universidade de São Paulo
  
  Universidade de São Paulo
  
  Brasil
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 2, 2013, págs. 377-391
Idioma: inglés
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Resumen
- Let f : T2 → T2 be a homeomorphism homotopic to the identity and F : R2 → R2 a lift of f such that the rotation set ρ(F) is a line segment of rational slope containing a point in Q2. We prove that if f is ergodic with respect to the Lebesgue measure on the torus and the average rotation vector (with respect to same measure) does not belong to Q2 then some power of f is an annular homeomorphism.