Continued Fractions, Interval Exchanges and Applications to Geometry
timetable:
Wed 12 Jun, 17:00 - 17:25, Aula Dini
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Continued fractions and multifractal analysis
speaker: Lingmin Liao (Université Paris-Est Créteil)abstract: We study the Gauss dynamical system associated to continued fractions from the point of view of multifractal analysis. First, we give the complete multifractal spectra of the Khinchine exponents and Lyapunov exponents of continued fractions. Then, we prove that the Hausdorff dimensions of the Besicovitch-Eggleston sets, which is the points with prescribed frequencies of partial quotients in their continued fraction expansions, are give by a modified variational principle. We also show that some sets of extremely non-mormal continued fractions are of Hausdorff dimension one-half. At last, we generalize the above results to some expanding interval maps with infinitely many branches.
timetable:
Wed 12 Jun, 17:00 - 17:25, Aula Dini
<< Go back