The rigidity conjecture

Fractal Geometry and Dynamics

29 November 14:00 - 14:50

Liviana Palmisano - University of Bristol

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.
Kenneth J. Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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