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 nonrigidity phenomena in a conjecture which describes how topological classes are organized into rigidity classes.
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The rigidity conjecture
Liviana Palmisano
Institution:
Uppsala University
Location:
Luigi Stasi Seminar Room, ICTP
Schedule:
Thursday, August 2, 2018  16:00
Abstract:
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