Centralizers of expanding maps on the circle
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- by Carlos Arteaga
- Proc. Amer. Math. Soc. 114 (1992), 263-267
- DOI: https://doi.org/10.1090/S0002-9939-1992-1070509-4
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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
- Carlos Arteaga, Centralizers of immersions of the circle, Proc. Amer. Math. Soc. 109 (1990), no.Β 3, 849β853. MR 1013962, DOI 10.1090/S0002-9939-1990-1013962-2
- Nancy Kopell, Commuting diffeomorphisms, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp.Β 165β184. MR 0270396
- Michael Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175β199. MR 240824, DOI 10.2307/2373276
- Shlomo Sternberg, Local $C^{n}$ transformations of the real line, Duke Math. J. 24 (1957), 97β102. MR 102581
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- 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