Dimension theory for continued fractions.

ABSTRACT: Every real number can be written as a continued fraction. There exists a dynamical system, the Gauss map, that acts as the shift in the expansion. In this talk, I will comment on the Hausdorff dimension of two types of sets: one of them defined in terms of arithmetic averages of the digits in the expansion and the other related to (continued fraction) normal numbers. In both cases, the non compactness that steams from the fact that we use countable many partial quotients in the continued fraction plays a fundamental role. Some of the results are joint work with Thomas Jordan and others together with Aníbal Velozo.

Posted on Aug 28, 2020 in Dynamical Systems, Seminars