4pm - 5pm
Friday 15 March 2019

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.


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