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arXiv · 1612.08939

The Rigidity Conjecture

Marco Martens·Liviana Palmisano·Björn Winckler
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Abstract

A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for 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. In this paper we state a conjecture which describes how topological classes are organized into rigidity classes.

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Marco Martens, Liviana Palmisano, Björn Winckler. 2016-12-28. The Rigidity Conjecture. https://doi.org/10.1016/j.indag.2017.08.001

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