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arXiv:1204.4843 [math.DS]AbstractReferencesReviewsResources

Dominated splitting for exterior powers of cocycles and singular hyperbolicity

Vitor Araujo, Luciana Salgado

Published 2012-04-21, updated 2015-01-17Version 5

We relate dominated splitting for a linear multiplicative cocyle with dominated splitting for the exterior powers of this cocycle. For a C1 vector field X on a 3-manifold, we can obtain singular-hyperbolicity using only the tangent map DX of X and a family of indefinite and non-degenerate quadratic forms without using the associated flow X_t and its derivative DX_t. As a consequence, we show the existence of adapted metrics for singular-hyperbolic sets for three-dimensional C1 vector fields.

Comments: 19 pages; major changes to the introduction and main statements with more precise results. 1 figure. Extra examples and counter-examples to certain higher-dimensional generalizations
Categories: math.DS, math.CA
Subjects: 37D30, 37D25
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