On the centralizer of diffeomorphisms of the half-line

Details On the centralizer of diffeomorphisms of the half-line On the centralizer of diffeomorphisms of the half-line

2008-11-07

arxiv.org/abs/0811.1173v1

Mathematics

Dynamical Systems

16 pages, 5 figures

Scientific paper

Let f be a smooth diffeomorphism of the half-line fixing only the origin and Z^r its centralizer in the group of C^r diffeomorphisms. According to well-known results of Szekeres and Kopell, Z^1 is a one-parameter group. On the other hand, Sergeraert constructed an f whose centralizer Z^r, $2\le r\le \infty$, reduces to the group generated by f. We show that Z^r can actually be a proper dense and uncountable subgroup of Z^1 and that this phenomenon is not scarce.

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