Department of Mathematics

DNA Seminar: The Rigidity Conjecture

  • Date: 11/24/2017 at 1:15 PM
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1
  • Lecturer: Liviana Palmisano
  • Contact person: Anders Öberg
  • Seminarium

Abstract: A central question in dynamics is whether the topology of a system determines its geometry, whether the system is rigid. Under mild topological conditions rigidity holds in many classical cases, including: Kleinian groups, circle diffeomorphisms, unimodal interval maps, critical circle maps, and circle maps with a break point. More recent developments show that under similar topological conditions, rigidity does not hold for slightly more general systems. We will discuss the case of circle maps with a flat interval. The class of maps with Fibonacci rotation numbers is a C1 manifold which is foliated with co dimension three rigidity classes. Finally, we summarize the known non-rigidity phenomena in a conjecture which describes how topological classes are organized into rigidity classes.