Mathematics

We will discuss the behaviour of orbits for chaotic dynamical systems and explore more generally how to analyse the distribution of collections of points generated by iterative procedures.  It turns out that these questions are related to several basic number-theoretical problems such as, for instance, solving polynomial equations and finding best rational approximations. We explain how to use these ideas to shed new light on the random-like behaviour of arithmetic objects. In this lecture, we will take a journey through Number Theory, Statistical Physics, the Theory of Dynamical Systems, and back.