An integral formula for the volume entropy with an application to rigidity (2009)
Ledrappier, Francois, Wang, Xiaodong
We extend the theory of Patterson-Sullivan measure to any regular covering of a compact manifold using the Busemann compactification and derive an integral formula for the volume entropy. As an...
Volume entropy of hyperbolic buildings (2009)
Ledrappier, Francois, Lim, Seonhee
We characterize the volume entropy of an arbitrary building as the topological pressure of the geodesic flow on an apartment. We show that the Liouville measure is not entropy maximizing measure for...
Martin points on open manifolds of non-positive curvature (2005)
Cao, Jianguo, Fan, Huijun, Ledrappier, Francois
The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric structure at infinity, which is a sub-space of positive harmonic functions. We describe conditions which ensure that some...
Random versus deterministic exponents in a rich family of diffeomorphisms (2002)
Ledrappier, Francois, Shub, Michael, Simo, Carles, Wilkinson, Amie
We study, both numerically and theoretically, the relationship between the random Lyapunov exponent of a family of area preserving diffeomorphisms of the 2-sphere and the mean of the Lyapunov...