Abstract

In this paper we introduce and consider the hyperbolic sets for the flows on pseudo-Riemannian manifolds. If $\Lambda $ is a hyperbolic set for a flow $\Phi $, then we show that at each point of $\Lambda $ we have a unique decomposition for its tangent space up to a distribution on the ambient pseudo-Riemannian manifold. We prove that we have such decomposition for many points arbitrarily close to a given member of $\Lambda $.

Keywords: Hyperbolic set; pseudo-Riemannian manifold; flow; distribution.

MSC: 37D20, 37D30

Pages:  117--123     

Volume  72 ,  Issue  2 ,  2020