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Law of large numbers for certain cylinder flows

Published online by Cambridge University Press:  23 January 2013

PATRÍCIA CIRILO ,
YURI LIMA  and
ENRIQUE PUJALS
PATRÍCIA CIRILO
Affiliation:
Universidade Estadual Paulista, Rua Cristóvão Colombo 2265, 15054-000, São José do Rio Preto, Brazil email prcirilo@ibilce.unesp.br
YURI LIMA
Affiliation:
Weizmann Institute of Science, Faculty of Mathematics and Computer Science, POB 26, 76100, Rehovot, Israel email yuri.lima@weizmann.ac.il
ENRIQUE PUJALS
Affiliation:
Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil email enrique@impa.br
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Abstract

We construct new examples of cylinder flows, given by skew product extensions of irrational rotations on the circle, that are ergodic and rationally ergodic along a subsequence of iterates. In particular, they exhibit a law of large numbers. This is accomplished by explicitly calculating, for a subsequence of iterates, the number of visits to zero, and it is shown that such number has a Gaussian distribution.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 3 , June 2014 , pp. 801 - 825
Copyright
©2013 Cambridge University Press 

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