  In this paper we study different notions of entropy for measure-preserving
dynamical systems defined on noncompact spaces. We see that some classical
results for compact spaces remain partially valid in this setting. We define a
new kind of entropy for dynamical systems defined on noncompact Riemannian
manifolds, which satisfies similar properties to the classical ones. As an
application, we prove Ruelle's inequality and Pesin's entropy formula for the
geodesic flow in manifolds with pinched negative sectional curvature.

Dynamical Systems