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Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes

Published online by Cambridge University Press:  03 February 2009

LORENZO J. DÍAZ  and
ANTON GORODETSKI
LORENZO J. DÍAZ
Affiliation:
Departamento de Matemática, PUC-Rio, Marquês de S. Vicente 225, 22453-900 Rio de Janeiro RJ, Brazil (email: lodiaz@mat.puc-rio.br)
ANTON GORODETSKI
Affiliation:
Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA (email: asgor@math.uci.edu)
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Abstract

We prove that there is a residual subset 𝒮 in Diff1(M) such that, for every f∈𝒮, any homoclinic class of f containing saddles of different indices (dimension of the unstable bundle) contains also an uncountable support of an invariant ergodic non-hyperbolic (one of the Lyapunov exponents is equal to zero) measure of f.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 5 , October 2009 , pp. 1479 - 1513
Copyright
Copyright © Cambridge University Press 2009

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