HYPERBOLIC SETS FOR THE FLOWS ON PSEUDO-RIEMANNIAN MANIFOLDS

Abstract

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