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Doctoral Thesis
DOI
10.11606/T.45.2012.tde-29082012-091937
Document
Author
Full name
Renato Belinelo Bortolatto
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Tal, Fabio Armando (President)
Carneiro, Mario Jorge Dias
Kocsard, Alejandro
Koropecki, Andrés
Zanata, Salvador Addas
Title in Portuguese
Ergodicidade e homeomorfismos anulares do toro
Keywords in Portuguese
conjuntos de rotação
ergodicidade
Homeomorfismos do toro
pontos periódicos
Abstract in Portuguese
Seja f : T2 -> T2 um homeomorfismo homotópico a identidade e F : R2 -> R2 um levantamento de f tal que seu conjunto de rotação rho(F) é um segmento vertical não degenerado contido em 0 × R. Provamos que se f é ergódico com respeito a medida de Lebesgue no toro e se o vetor de rotação médio (com respeito a mesma medida) é da forma (0, alpha) para alpha em R\Q então existe M > 0 tal que |(Fn (x) - x)1| <= M para todo x em R2 e n em Z (onde (.)1 :R2 -> R é definida por (x,y)1 =x).
Title in English
Ergodicity and annular homeomorphism of the torus
Keywords in English
ergodicity
periodic points
rotation sets
Torus homeomorphisms
Abstract in English
Let f : T2 -> T2 be a homeomorphism homotopic to the identity and F : R2 -> R2 a lift of f such that the rotation set rho(F) is a non-degenerated vertical line segment contained in 0 × R. 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) is of the form (0, alpha) for alpha in R\Q then there exists M > 0 such that |(Fn (x) - x)1| <= M for all x in R2 and n in Z (where (.)1 :R2 -> R is defined by (x, y)1 = x).
 
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EHAT.pdf (559.20 Kbytes)
Publishing Date
2012-09-10
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • Bortolatto, R. B., and TAL, F. A. Ergodicity and Annular Homeomorphisms of the Torus [doi:10.1007/s12346-012-0095-8]. Qualitative Theory of Dynamical Systems [online], 2012, vol. online, p. 1.
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