Ergodic Theory and Dynamical Systems: Volume 2 -

Entropy estimates for geodesic flows
P. Sarnak
Published online by Cambridge University Press:

19 September 2008, pp. 513-524
- Article
- - You have access
- PDF
- Export citation
Let M be a compact Riemannian manifold of (variable) negative curvature. Let h be the topological entropy and hμ the measure entropy for the geodesic flow on the unit tangent bundle to M. Estimates for h and hμ in terms of the ‘geometry’ of M are derived. Connections with and applications to other geometric questions are discussed.

On the ergodic properties of piecewise linear perturbations of the twist map
M. Wojtkowski
Published online by Cambridge University Press:

19 September 2008, pp. 525-542
- Article
- - You have access
- PDF
- Export citation
It is proved that for a sequence of arbitrarily small piecewise linear perturbations of the twist map, there is a domain with stochastic behaviour (almost hyperbolicity). The measure of this domain has the asymptotics
where A is the magnitude of the perturbation.

Ergodic Theory and Dynamical Systems