Counterexamples to Ruelle's inequality in the noncompact case

Felipe Riquelme (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we show that there exists a large family of smooth dynamical systems defined over noncompact spaces that does not satisfy Ruelle's inequality between entropy and Lyapunov exponents.

Mots clés: Ergodic Theory; Riemannian Geometry; smooth dynamical systems; Lyapunov exponents; Ruelle's Inequality

Domaines: Systèmes dynamiques [math.DS]

Felipe Riquelme. Counterexamples to Ruelle's inequality in the noncompact case. Annales de l'Institut Fourier, 2017, 67 (1), pp.23-41. ⟨10.5802/aif.3076⟩. ⟨hal-01212973v2⟩