Adapted Metrics for Codimension one Singular Hyperbolic Flows
arXiv:1707.09249 · doi:10.1007/978-3-030-16833-9
Abstract
For a partially hyperbolic splitting a vector field on a -manifold , we obtain singular hyperbolicity whether 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 , where is a volume expanding subbundle, is an uniformly contracted and one-dimensional subbundle. Theses results extend previous ones from the first author and V. Araújo.
17 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1204.4843