Mathematical Sciences Research Seminar Series

Complete spectral data for certain families of expanding and hyperbolic maps

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Seminars

As part of the School of Science and Technology Mathematical Sciences Research Seminar Series, Dr Julia Slipantschuk, Queen Mary University of London presents: Complete spectral data for certain families of expanding and hyperbolic maps.

  • From: Wednesday 6 March 2019, 1 pm
  • To: Wednesday 6 March 2019, 2 pm
  • Location: 169, New Hall Block, Nottingham Trent University, Clifton Campus, Clifton Lane, Nottingham, NG11 8NS

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Event details

As part of the School of Science and Technology Mathematical Sciences Research Seminar Series, Dr Julia Slipantschuk, Queen Mary University of London presents: Complete spectral data for certain families of expanding and hyperbolic maps.

Abstract

A powerful approach for the study of the statistical long-term behaviour of dynamical systems consists of reformulating the problem in terms of spectral properties of the (Ruelle-)Perron Frobenius operator. This operator describes how a distribution of initial points evolves under the action of the underlying dynamics, thus providing global representation of system’s dynamics. Moreover, its spectrum yields insight into the fine statistical properties such as possible rates rates of mixing (rates of decay of correlations). Surprisingly there exist only few examples of maps in the literature for which the spectrum of the corresponding transfer operator is known explicitly. The purpose of this talk is to present families of (nonlinear) expanding circle maps as well as families of hyperbolic toral diffeomorphisms for which the spectra of the associated transfer operator acting on suitable Hilbert spaces can be computed explicitly.

All Welcome

For any enquiries please contact Dr David Chappell.

Location details

Room/Building:

169, New Hall Block

Address:

Nottingham Trent University
Clifton Campus
Clifton Lane
 Nottingham
 NG11 8NS

Past event

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