DNA seminar: Zero-one laws for uniform shrinking target systems

  • Date: –11:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Ioannis Konstantoulas
  • Organiser: Matematiska institutionen
  • Contact person: Andreas Strömbergsson
  • Seminarium

Abstract: In this talk we will motivate and review shrinking target systems in dynamics and introduce a uniform version that reflects the long term behavior of large orbital segments in systems with high independence.  Our main theorem is a zero-one law for the Eventually Always Hitting set, applicable to settings such as Bernoulli systems, uniform Diophantine approximation and the Gauss map.  

Unlike the classical setting, we will see that the uniform zero-one law is highly sensitive to the 'geometry' of the targets and thus expresses much more of the structure of the specific system.  

This is joint work with Dmitry Kleinbock and Florian Richter.