Explicit Ruelle resonances of chaotic dynamical systems

Speaker: Oscar Bandtlow (Queen Mary University, London)

Abstract: 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

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.