Géométrie et dynamique dans les espaces de modules

Séminaire Mensuel

Séminaire - Novembre

Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris.  Pour télécharger le programme du mois: novembre.pdf.

  • 16/11/2016 - Luca Marchese  (Université  Paris 13)  -  salle 421

  • Titre: Existence of Hall ray in the Lagrange spectrum of Fuchsian groups with cusps and finite co-volume.

    Resumé: The classical Lagrange spectrum is a subset of the positive real line and corresponds to a filtration of the set of badly approximable real numbers. Elements in the spectrum can also be interpreted in term of asymptotic penetration into the cusp of some bounded positive geodesic ray on the modular surface. Well known subsets of the spectrum are for example Markov’s numbers, that is its discrete lower part, or Hall’s ray, that is its upper part, which is an entire positive half-line. Many generalization exist in dynamics, and in this talk we consider a very natural one replacing the modular surface with any quotient of the upper half plane by a Fuchsian group with cusps and finite co-volume, and considering the geodesic flow on the quotient space. We prove the existence of Hall ray in this generalized setting. This is a joint work with M. Artigiani and C. Ulcigrai.