Entropies for a diffeomorphism on a noncompact manifold. Applications to Ruelle's inequality and Pesin's formula.

Felipe Riquelme (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we study different notions of entropy of 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 for the geodesic flow in manifolds with pinched negative curvature. We discuss the case of equality and we give some corollaries.

Mots clés: Lyapunov exponents.; Geodesic flow; Gibbs measure; Entropy

Domaines: Systèmes dynamiques [math.DS]

Felipe Riquelme. Entropies for a diffeomorphism on a noncompact manifold. Applications to Ruelle's inequality and Pesin's formula.. 2016. ⟨hal-01254491v1⟩