On the Lagrange and Markov Dynamical Spectra for Geodesic Flows in Surfaces with Negative Curvature

Abstract

We consider the Lagrange and the Markov dynamical spectra associated to a geodesic flow on a surface of negative curvature. We show that for a large set of real functions on the unit tangent bundle and for typical metrics with negative curvature and finite volume, both the Lagrange and the Markov dynamical spectra have non-empty interior.

Final Version

References in corpus (1)

• Persistent Hall rays for Lagrange spectra at cusps of Riemann surfaces

Cited by in corpus (2)

• Homoclinic Bifurcations: our collaboration with Jean-Christophe Yoccoz
• The Lagrange spectrum of some square-tiled surfaces