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Dynamics of generic 2-dimensional linear differential systems

Publication . Bessa, Mário

We prove that for a C0-generic (a dense Gδ) subset of all the 2-dimensional conservative nonautonomous linear differential systems, either Lyapunov exponents are zero or there is a dominated splitting μ almost every point.

2006Journal article

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

Publication . Bessa, Mário

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.

2007Journal article

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