The C 1 generic diffeomorphism has trivial centralizer
Publications Mathématiques de l'IHÉS, Volume 109  (2009), p. 185-244

Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.

@article{PMIHES_2009__109__185_0,
     author = {Bonatti, Christian and Crovisier, Sylvain and Wilkinson, Amie},
     title = {The C 1 generic diffeomorphism has trivial centralizer},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer-Verlag},
     volume = {109},
     year = {2009},
     pages = {185-244},
     doi = {10.1007/s10240-009-0021-z},
     zbl = {1177.37025},
     mrnumber = {2511588},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2009__109__185_0}
}
Bonatti, Christian; Crovisier, Sylvain; Wilkinson, Amie. The C 1 generic diffeomorphism has trivial centralizer. Publications Mathématiques de l'IHÉS, Volume 109 (2009) , pp. 185-244. doi : 10.1007/s10240-009-0021-z. http://www.numdam.org/item/PMIHES_2009__109__185_0/

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