  We consider a discrete dynamical system on a pseudo-Riemannian manifold and
we determine the concept of a hyperbolic set for it. We insert a condition in
the definition of a hyperbolic set which implies to the unique decomposition of
a part of tangent space (at each point of this set) to two unstable and stable
subspaces with exponentially increasing and exponentially decreasing dynamics
on them. We prove the continuity of this decomposition via the metric created
by a torsion-free pseudo-Riemannian connection. We present a global attractor
for a diffeomorphism on an open submanifold of the hyperbolic space $H^{2}(1)$
which is not a hyperbolic set for it.
