Symbolic dynamics and arithmetic expansions

A dynamical system is a mathematical model of a time-dependent process. Classic examples are the movement of a pendulum, the movement of a planet in the solar system or so-called predator-prey systems. Dynamical systems also play a major role in pure mathematics. For example, representations of numbers using digits (such as in the decimal system or the binary system, which is particularly important in computer science) or so-called continued fractions can be modeled using dynamical systems. The study of such "arithmetic" dynamical systems has a long tradition in both France and Austria, which is also characterized by intensive cooperation between researchers from both countries. This project aims to further strengthen this cooperation. In an ambitious four-year program, new results are to be achieved in the field of arithmetic dynamical systems, the significance of which goes far beyond applications in mathematics and extends, for example, into computer science or physics. The organization of international conferences and workshops is also intended to facilitate an intensive exchange of scientists from all over the world in order to provide further incentives for future research in this important field.