Ruelle transfer operators with explicit spectra

Jeudi 7 juin 2018 14:00-15:00 - Oscar Bandtlow - Queen Mary University

Résumé : In a seminal paper Ruelle showed that the long time asymptotic behaviour of analytic hyperbolic systems can be understood in terms of the eigenvalues, also known as Pollicott-Ruelle resonances, of the so-called Ruelle transfer operator, a compact operator acting on a suitable Banach space of holomorphic functions.
Until recently, there were no examples of Ruelle transfer operators arising from analytic hyperbolic circle or toral maps, with non-trivial spectra, that is, spectra different from 0,1.
In this talk I will survey recent work with Wolfram Just and Julia Slipantschuk on how to construct analytic expanding circle maps or analytic Anosov diffeomorphisms on the torus with explicitly computable non-trivial Pollicott-Ruelle resonances. I will also discuss applications of these results.

Lieu : IMO, salle 2L8

Notes de dernières minutes : Café culturel à 13h par Hans-Henrik Rugh

Ruelle transfer operators with explicit spectra  Version PDF