Doktorandseminarium: Circle maps, small divisors and some KAM theory

  • Datum:
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Victor Linroth
  • Kontaktperson: Volodymyr Mazorchuk
  • Seminarium

Abstract: I will briefly introduce the topic of circle maps, in particular circle homeomorphisms and diffeomorphisms. It's a classical result by Poincare that transitive circle homemorphisms are homeomorphically conjugated to rigid rotations and one can then ask in what way this can be extended to the diffeomorphism case. One of the early results is Arnold's theorem for analytic circle maps and the proof is an application of KAM theory. This is probably the simplest case for which one case showcase KAM theory and such it servers as good entry point for those not familiar with the subject. In the proof one also encounters the problem of small divisors which is common in dynamical systems, and we will see how to overcome this using Diophantine numbers.