Entropy estimates for geodesic flows

Peter Sarnak

Type: Article

Publication Date: 1982-12-01

Citations: 13

DOI: https://doi.org/10.1017/s0143385700001747

Abstract

Abstract Let M be a compact Riemannian manifold of (variable) negative curvature. Let h be the topological entropy and h μ the measure entropy for the geodesic flow on the unit tangent bundle to M . Estimates for h and h μ in terms of the ‘geometry’ of M are derived. Connections with and applications to other geometric questions are discussed.

Locations

Ergodic Theory and Dynamical Systems - View - PDF
Ergodic Theory and Dynamical Systems - View - PDF
Ergodic Theory and Dynamical Systems - View - PDF

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Works Cited by This (7)

Action	Title	Year	Authors
+ PDF	Curvature and the eigenvalues of the Laplacian	1967	H. P. McKean I. M. Singer
+ PDF	An upper bound to the spectrum of $\Delta $ on a manifold of negative curvature	1970	H. P. McKean
+	Topological Entropy for Geodesic Flows	1979	Anthony Manning
+ PDF	Entropy and closed geodesies	1982	A. Katok
+	Applications of ergodic theory to the investigation of manifolds of negative curvature	1970	G. A. Margulis
+	Introduction to ergodic theory	1976	Я.Г. Синай Vladimir Scheffer
+ PDF	When is a geodesic flow of Anosov type? I	1973	Patrick Eberlein