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Minimal non-ergodic C^1-diffeomorphisms of the circle

Published online by Cambridge University Press:  28 November 2001

FERNANDO OLIVEIRA and
L. F. C. DA ROCHA
FERNANDO OLIVEIRA
Affiliation:
Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Av. Antonio Carlos, 6627, CEP 30123-970, Belo Horizonte/MG, Brazil (e-mail: fernando@mat.ufmg.br)
L. F. C. DA ROCHA
Affiliation:
Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Goncalves 9500, CEP 91500, Porto Alegre/RS, Brazil (e-mail: rocha@mat.ufrgs.br)
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Abstract

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We construct, for each irrational number \alpha, a minimal C^1-diffeomorphism of the circle with rotation number \alpha which is not ergodic with respect to the Lebesgue measure.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 6 , December 2001, pp. 1843 - 1854
Copyright
2001 Cambridge University Press