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.