Local density of diffeomorphisms with large centralizers

Christian Bonatti; Sylvain Crovisier; Gioia M. Vago; Amie Wilkinson

Annales scientifiques de l'École Normale Supérieure (2008)

  • Volume: 41, Issue: 6, page 925-954
  • ISSN: 0012-9593

Abstract

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Given any compact manifold M , we construct a non-empty open subset 𝒪 of the space Diff 1 ( M ) of C 1 -diffeomorphisms and a dense subset 𝒟 ⊂ 𝒪 such that the centralizer of every diffeomorphism in 𝒟 is uncountable, hence non-trivial.

How to cite

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Bonatti, Christian, et al. "Local density of diffeomorphisms with large centralizers." Annales scientifiques de l'École Normale Supérieure 41.6 (2008): 925-954. <http://eudml.org/doc/272105>.

@article{Bonatti2008,
abstract = {Given any compact manifold $M$, we construct a non-empty open subset $\mathcal \{O\}$ of the space $\mathrm \{Diff\}^1(M)$ of $C^1$-diffeomorphisms and a dense subset $\mathcal \{D\}\subset \mathcal \{O\}$ such that the centralizer of every diffeomorphism in $\mathcal \{D\}$ is uncountable, hence non-trivial.},
author = {Bonatti, Christian, Crovisier, Sylvain, Vago, Gioia M., Wilkinson, Amie},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {trivial centralizer; trivial symmetries; Mather invariant},
language = {eng},
number = {6},
pages = {925-954},
publisher = {Société mathématique de France},
title = {Local density of diffeomorphisms with large centralizers},
url = {http://eudml.org/doc/272105},
volume = {41},
year = {2008},
}

TY - JOUR
AU - Bonatti, Christian
AU - Crovisier, Sylvain
AU - Vago, Gioia M.
AU - Wilkinson, Amie
TI - Local density of diffeomorphisms with large centralizers
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2008
PB - Société mathématique de France
VL - 41
IS - 6
SP - 925
EP - 954
AB - Given any compact manifold $M$, we construct a non-empty open subset $\mathcal {O}$ of the space $\mathrm {Diff}^1(M)$ of $C^1$-diffeomorphisms and a dense subset $\mathcal {D}\subset \mathcal {O}$ such that the centralizer of every diffeomorphism in $\mathcal {D}$ is uncountable, hence non-trivial.
LA - eng
KW - trivial centralizer; trivial symmetries; Mather invariant
UR - http://eudml.org/doc/272105
ER -

References

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