Partially hyperbolic geodesic flows
Dynamical Systems
2013-03-12 v3
Abstract
We construct a category of examples of partially hyperbolic geodesic flows which are not Anosov, deforming the metric of a compact locally symmetric space of nonconstant negative curvature. Candidates for such example as the product metric and locally symmetric spaces of nonpositive curvature with rank bigger than one are not partially hyperbolic. We prove that if a metric of nonpositive curvature has a partially hyperbolic geodesic flow, then its rank is one. Other obstructions to partial hyperbolicity of a geodesic flow are also analyzed.
Cite
@article{arxiv.1110.1050,
title = {Partially hyperbolic geodesic flows},
author = {Fernando A. Carneiro and Enrique R. Pujals},
journal= {arXiv preprint arXiv:1110.1050},
year = {2013}
}
Comments
42 pages