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.

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