Matematiska institutionen

Weighted Birkhoff Averages for Quasiperiodic Quadrature

  • Datum: 2017-02-22 kl 13:15
  • Plats: Ångströmlaboratoriet
  • Föreläsare: Victor Linroth
  • Kontaktperson: Volodymyr Mazorchuk
  • Seminarium

Doktorandseminarium

Abstract:

The Birkhoff Ergodic theorem is a classic result that lets us use an ergodic dynamical system to numerically calculate integrals with respect to the invariant measure by taking averages over orbits. For most practical cases this is not a very good way calculate integrals numerically because for a general ergodic system the rate of convergence can be arbitrarily slow. However it has recently been discovered that if the system is conjugate to a quasiperiodic rotation then by applying a simple weighting to the average we can get a super-polynomial convergence rate. I'll show the rather simple proof of this and also some applications where these types of integrals appear.