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.
Original language | English |
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Pages (from-to) | 825-830 |
Number of pages | 6 |
Journal | Indagationes Mathematicae |
Volume | 29 |
Issue number | 3 |
Early online date | 26 Aug 2017 |
DOIs | |
Publication status | Published - Jun 2018 |
Keywords
- Rigidity
- Renormalization
- Smooth dynamics