Abstract.
In the context of Cr-flows on 3-manifolds (r ≥ 1), the notion of singular hyperbolicity, inspired on the Lorenz Attractor, is the right generalization of hyperbolicity (in the sense of Smale) for C1-robustly transitive sets with singularities. We estabish conditions (on the associated linear Poincaré flow and on the nature of the singular set) under which a transitive attractor with singularities of a C2-flow on a 3-manifold is singular hyperbolic.
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Arroyo, A. Singular hyperbolicity for transitive attractors with singular points of 3-dimensional C2-flows. Bull Braz Math Soc, New Series 38, 455–465 (2007). https://doi.org/10.1007/s00574-007-0055-0
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DOI: https://doi.org/10.1007/s00574-007-0055-0