CRM: Centro De Giorgi
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Renormalization in Dynamics - Pisa 2016

The lower part of some generalized Lagrange spectrum

speaker: Luca Marchese (Université Paris 13)

abstract: The classical Lagrange spectrum is a subset of the positive half line corresponding to a filtration of the set of badly approximable real numbers. The elements in the spectrum can be expressed also as maximal asymptotic excursion of bounded geodesics on the modular surface, which is the moduli space of flat tori. The smallest element of the spectrum is \sqrt{5}, followed by a discrete sequence convergent to 3, elements in this discrete part being in bijection with Markoff numbers. Replacing the modular surface by the moduli space of translation surfaces, or any of its SL(2,R)-invariant submanifolds, we can define a generalized Lagrange spectrum as the set of maximal asymptotic excursion of bounded geodesics inside the invariant manifold. These generalized spectra share several properties with the classical one, but some new phenomana also appear. In particular, in this talk it is considered an invarian manifold whose Lagrange spectrum has an isolated minimum, but no discrete part right above it. Joint work with P. Hubert, S. Lelièvre, C. Ulcigrai.

Mon 4 Apr, 17:00 - 17:45, Aula Dini
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