Centralizers of C^1-generic diffeomorphisms
Abstract
On the one hand, we prove that the spaces of C^1 symplectomorphisms and of C^1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of C^1 diffeomorphisms of the circle and a non-empty open set of C^1 diffeomorphisms of the two-sphere contain dense subsets of diffeomorphisms whose centralizer has a sub-group isomorphic to R.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- October 2006
- DOI:
- 10.48550/arXiv.math/0610064
- arXiv:
- arXiv:math/0610064
- Bibcode:
- 2006math.....10064B
- Keywords:
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- Mathematics - Dynamical Systems