CRM: Centro De Giorgi
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Seminari di Sistemi Dinamici Olomorfi 2018-2019

seminar: Lower bounds for the Ruelle eigenvalues of analytic circle maps

speaker: Oscar Bandtlow (Queen Mary University of London)

abstract: In a seminal paper Ruelle showed that the long time asymptotic behaviour of analytic hyperbolic systems can be understood in terms of the eigenvalues of a certain operator acting on a suitable Banach space of holomorphic functions. Ruelle also showed that these eigenvalues, also known as Pollicott-Ruelle resonances, are bounded from above by a decaying exponential.

In this talk I will focus on lower bounds for the Ruelle eigenvalues. More precisely, I will explain how to prove that there exists a dense set of analytic expanding circle maps for which the Ruelle eigenvalues enjoy exponential lower bounds.

This is based on work with W. Just, J. Slipantschuk, and F. Naud.

Wed 15 May, 15:00 - 16:00, Sala Conferenze Centro De Giorgi
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