On dynamical Lagrange and Markov spectra.

Carlos Matheus (Paris 13)

Monday 3rd October, 2016 16:00-17:00 Maths 522

Abstract

The classical Lagrange and Markov spectra have their origin in some Diophantine approximation problems. As we are going to recall in the introductory part of this talk, these spectra are an important particular case of the dynamical Lagrange and Markov spectra describing the heights of orbits of a given system. After this, we will proceed to the discussion of the main result of the talk, namely, we will show that the Hausdorff dimension varies continuously across dynamical Lagrange and Markov spectra associated to horseshoes of a typical surface diffeomorphism and a generic height function.

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