Dominated splitting for exterior powers and singular hyperbolicity
arXiv:1204.4843 · doi:10.1016/j.jde.2015.05.006
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.
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. Streamlined presentation to motivate mais results. arXiv admin note: text overlap with arXiv:1201.2550