Location:

Alte UniversitÃ¤t, Rheinsprung 9, Lecture Hall -101

Organizer:

Mathematics

## Public Inaugural Lecture PD Dr. Jung-Kyu Canci: Dynamical systems with a view toward arithmetic

A dynamical system is essentially the repeated iteration of an action.

The study of dynamical systems has a long history. Many people consider Henri PoincarÃ© as the founder (at the end of the 19th century) of the modern theory of dynamical systems. Further important contributions at the beginning of the 20th are due to George David Birkhoff, Gaston Julia and Pierre Fatou.

In the talk we will discuss some aspects of the theory of dynamical systems with a view toward arithmetic. As an example we will show that Birkhoff's multiple recurrence Theorem can be used to provide an alternative proof of van der Waerden's Theorem on arithmetic progressions. We will also show that Julia sets are useful to understand the dynamic given by a rational function.

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