Abstract
We prove here that the elements of an open and dense subset of expanding maps on tori have trivial centralizers; i.e., the maps commute only with their own powers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Anderson,Diffeomorphisms with discrete centralizer. Topology,15 (1976), 143–147.
C. Arteaga,Centralizers of immersions of the circle. Proc. of the Amer. Math. Soc.109 (1990), 849–853.
C. Arteaga,Centralizers of expanding maps of the circle. Proc. of the Amer. Math. Soc.114 (1992), 263–267.
M. Craizer,Teoria Ergódica das Transformações Expansoras. Inf. de Mat., IMPA, E-018 (1985).
N. Kopell,Commuting Diffeomorphisms. Global Analysis14 (1970), 165–185.
J. Palis & J. C. Yoccoz,Centralizers of Anosov Diffeomorphisms on Tori. Ann. Scient. Ec. Norm. Sup. 4aSerie22 (1989), 81–98.
M. Shub,Endomorphisms of compact Differentiable Manifolds. Amer. J. Math.91 (1969), 175–199.
Author information
Authors and Affiliations
Additional information
The author was partially supported by CNPq, Brazil.
About this article
Cite this article
Arteaga, C. Centralizers of expanding maps on tori. Bol. Soc. Bras. Mat 26, 149–159 (1995). https://doi.org/10.1007/BF01236990
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01236990