Many clever techniques have been developed to study the particular parabolic dynamics of multidimensional continued fractions and Rauzy inductions in the past decades. I will present a work that aims to unify the description of this class of systems by associating a directed graph to each of them. The study of their dynamics is then reduced to understanding a random walk on these graphs. These random walks are quite original objects since they have an infinite memory encoded in a vector.
In a first part I will give a survey of multidimensional continued fraction algorithms and Rauzy inductions with elementary computations on examples that show the link with a random walk on a graph. After the break I will explain a result that relates their dynamical properties (ergodicity, measure of maximal entropy, ...) with a property on their graphs.
Continued fractions, Rauzy inductions and random walks
15.06.2023 15:00 - 17:00
Organiser:
H. Bruin, R. Zweimüller
Location: