Infinitesimal Lyapunov functions and singular-hyperbolicity for three-dimensional flows

Details Infinitesimal Lyapunov functions and singular-hyperbolicity for three-dimensional flows Infinitesimal Lyapunov functions and singular-hyperbolicity for three-dimensional flows

2012-04-21

arxiv.org/abs/1204.4843v1

Mathematics

Dynamical Systems

14 pages

Scientific paper

We use the notion of infinitesimal Lyapunov function applied to three-dimensional singular vector fields, obtaining a characterization of singular-hyperbolicity using the vec- tor field X, its space derivative DX and a family of non-degenerate indefinite quadratic forms only. This improves other results from the authors where the same conclusion was obtained through the Linear Poincare flow, which is only defined away from singularities.

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