Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Centralizers of expanding maps on the circle


Author: Carlos Arteaga
Journal: Proc. Amer. Math. Soc. 114 (1992), 263-267
MSC: Primary 58D10; Secondary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1992-1070509-4
MathSciNet review: 1070509
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove here that the elements of an open and dense subset of expanding maps on the circle have trivial centralizers; i.e., the maps commute only with their own powers. Using a theorem proved in [1], we deduce that the result is also true for an open and dense subset of immersions of $ {S^1}$.


References [Enhancements On Off] (What's this?)

  • [1] C. Arteaga, Centralizers of immersions of the circle, Proc. Amer. Math. Soc. 109 (1990), 849-853. MR 1013962 (90k:58099)
  • [2] N. Kopell, Commuting diffeomorphisms, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, RI, 1970, pp. 165-184. MR 0270396 (42:5285)
  • [3] M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175-199. MR 0240824 (39:2169)
  • [4] S. Sternberg, Local $ {C^n}$ transformations of the real line, Duke Math. J. 24 (1957), 97-102. MR 0102581 (21:1371)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58D10, 54H20

Retrieve articles in all journals with MSC: 58D10, 54H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1070509-4
Keywords: Expanding maps, centralizer, trivial centralizer
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society