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The Lyapunov exponents of generic zero divergence three-dimensional vector fields

Published online by Cambridge University Press:  01 October 2007

MÁRIO BESSA
MÁRIO BESSA*
Affiliation:
IMPA, Estr. D. Castorina 110, 22460-320 Rio de Janeiro, Brazil (email: bessa@impa.br)
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Abstract

We prove that for a C1-generic (dense Gδ) subset of all the conservative vector fields on three-dimensional compact manifolds without singularities, we have for Lebesgue almost every (a.e.) point p∈M that either the Lyapunov exponents at p are zero or X is an Anosov vector field. Then we prove that for a C1-dense subset of all the conservative vector fields on three-dimensional compact manifolds, we have for Lebesgue a.e. p∈M that either the Lyapunov exponents at p are zero or p belongs to a compact invariant set with dominated splitting for the linear Poincaré flow.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 5 , October 2007 , pp. 1445 - 1472
Copyright
Copyright © Cambridge University Press 2007

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