Florin Boca
University of Illinois at Urbana-Champaign, USA

The periodic points of the Gauss map coincide with the reduced quadratic irrationals, known to be related with the Pell equation and with closed geodesics on the modular surface. Classical work of Pollicott proved uniform distribution of these numbers with respect to the Gauss probability measure, when ordered by their associated closed primitive geodesic length. An effective version was established more recently by Ustinov. This talk will discuss the distribution of periodic points of Gauss type shifts arising from other types of Euclidean continued fractions and the corresponding classes of reduced quadratic irrationals. This is joint work with Maria Siskaki.