# The rigidity conjecture

 Orateur: PALMISANO Liviana Localisation: Université de Bristol, Royaume-Uni Type: Séminaire COOL Site: Hors LAMA , IHP Salle: 05 Date de début: 08/12/2017 - 14:00 Date de fin: 08/12/2017 - 14:00

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 $C^1$ 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.