Centralizers of immersions of the circle
Proc. Amer. Math. Soc. 109 (1990), 849-853
Primary 58F10; Secondary 20F38, 58D10
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Abstract: We prove here that for every element of an open and dense subset of immersions of the circle , either the centralizer of is trivial (i.e. only commutes with its own powers) or is topologically conjugate to a map given by and, in this case, if is the conjugacy between and then is a subgroup of .
V. Jakobson, Smooth mappings of the circle into itself, Mat.
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Kopell, Commuting diffeomorphisms, Global Analysis (Proc.
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Providence, R.I., 1970, pp. 165–184. MR 0270396
Mañé, Hyperbolicity, sinks and measure in
one-dimensional dynamics, Comm. Math. Phys. 100
(1985), no. 4, 495–524. MR 806250
- M. V. Jacobson, On smooth mappings of the circle into itself, Math. USSR-Sb. 14 (1971), 163-168. MR 0290406 (44:7587)
- N. Kopell, Commuting diffeomorphisms, Global Analysis, Proc. Sympos. Pure Math. 14 (1970), 165-184. MR 0270396 (42:5285)
- R. Mañe, Hyperbolicity, sinks and measure in one dimensional dynamics, Comm. Math. Phys. 100 (1985), 495-524. MR 806250 (87f:58131)
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