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Non-existence of sublinear diffusion for a class of torus homeomorphisms

Part of: Low-dimensional dynamical systems

Published online by Cambridge University Press:  18 January 2021

GUILHERME SILVA SALOMÃO  and
FABIO ARMANDO TAL
GUILHERME SILVA SALOMÃO
Affiliation:
Instituto de Matemática e Estatística, Rua do Matão 1010, Cidade Universitária, São Paulo, SP, Brazil, 05508-090 (e-mail: salomao.guilherme@gmail.com)
FABIO ARMANDO TAL*
Affiliation:
Instituto de Matemática e Estatística, Rua do Matão 1010, Cidade Universitária, São Paulo, SP, Brazil, 05508-090 (e-mail: salomao.guilherme@gmail.com)
*
e-mail: fabiotal@ime.usp.br
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Abstract

We prove that, if f is a homeomorphism of the 2-torus isotopic to the identity whose rotation set is a non-degenerate segment and f has a periodic point, then it has uniformly bounded deviations in the direction perpendicular to the segment.

Keywords

rotation setsforcingbounded deviations

MSC classification

Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 37E45: Rotation numbers and vectors
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 4 , April 2022 , pp. 1517 - 1547
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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