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- W1609944452 abstract "Let f be a smooth diffeomorphism of the half-line fixing only the origin and Z^r_f its centralizer in the group of C^r diffeomorphisms. According to well-known results of Szekeres and Kopell, Z^1_f is always a one-parameter group, naturally identified to R, (with f identified to 1). On the other hand, Z^r_f, for r greater or equal to 2, can be smaller: in [Se], Sergeraert constructed an f whose C^infty centralizer reduces to the infinite cyclic group generated by f (i.e Z^infty_f identifies to Z). In [Ey1], we adapted Sergeraert's construction to obtain an f whose C^r centralizer, for all r between 2 and infty, contains a Cantor set K but is still strictly smaller than Z^1_f (= R). Here, we improve [Ey1] to construct, for any Liouville number alpha, an f as above such that, in addition, alpha belongs to K." @default.
- W1609944452 created "2016-06-24" @default.
- W1609944452 creator A5038779466 @default.
- W1609944452 date "2010-11-15" @default.
- W1609944452 modified "2023-09-26" @default.
- W1609944452 title "Arithmetic properties of centralizers of diffeomorphisms of the half-line" @default.
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