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arXiv · 1204.4843

Dominated splitting for exterior powers and singular hyperbolicity

Vitor Araujo·Luciana Salgado
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Abstract

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.

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Vitor Araujo, Luciana Salgado. 2012-04-21. Dominated splitting for exterior powers and singular hyperbolicity. https://doi.org/10.1016/j.jde.2015.05.006

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