Institut für Mathematik


Konferenz: Symposium about Pure Mathematics

Chaos and Order in Arithmetics and Dynamics

Vortrag von Prof. Dr. Alexander Gorodnik
Datum: 09.02.17   Zeit: 08.30 - 09.10   Raum: Y27H28

We will discuss behaviour of chaotic group actions and explore how to analyse statistical properties of collections of points generated by iterative procedures. It turns out that this question is related to several fundamental number-theoretical problems such as, for instance, solving polynomial equations and finding best rational approximations. It is difficult and sometimes impossible to solve these problems explicitly, but it turns out thatthey are related to certain chaotic dynamical systems. We explain how to use these ideas to shed some light on statistical properties of solutions. In this lecture we will take a journey through Number Theory, Statistical Physics, the Theory of Dynamical Systems, and back.