In a seminal paper Ruelle showed that the long time asymptotic 
behaviour of certain chaotic dynamical systems can be understood in 
terms of the eigenvalues, also known as Ruelle resonances, of the 
so-called Ruelle transfer operator, a linear operator acting on a suitable 
Banach space of functions defined on the phase space of the underlying 
dynamical system.

There is by now a considerable body of results on properties of Ruelle 
resonanaces for given classes of dynamical systems. However, until 
recently there were very few examples of dynamical systems for which 
the Ruelle resonances could be calculated explicitly.

In this talk I will provide an introduction to Ruelle resonances 
accessible to a general mathematical audience followed by a survey 
of recent work with Wolfram Just and Julia Slipantschuk on how to construct 
expanding circle maps or analytic Anosov diffeomorphisms on the torus with 
explicitly computable Ruelle resonances.

Einladung von Prof. Anke Pohl