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arXiv · 1707.09249

Adapted Metrics for Codimension one Singular Hyperbolic Flows

Luciana Salgado·Vinicius Coelho
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Abstract

For a partially hyperbolic splitting a $C^1$ vector field $X$ on a $m$-manifold $M$, we obtain singular hyperbolicity whether $E$ is one-dimensional subspace, based on the idea of cross products. We show the existence of adapted metrics for singular hyperbolic set if it has a partially hyperbolic splitting $T_{\Gamma}M = E \oplus F$, where $F$ is a volume expanding subbundle, $E$ is an uniformly contracted and one-dimensional subbundle. Theses results extend previous ones from the first author and V. Ara\'ujo.

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Luciana Salgado, Vinicius Coelho. 2017-07-26. Adapted Metrics for Codimension one Singular Hyperbolic Flows. https://doi.org/10.1007/978-3-030-16833-9

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