On the centralizer of diffeomorphisms of the half-line
Abstract
Let f be a smooth diffeomorphism of the half-line fixing only the origin and Zr its centralizer in the group of Cr diffeomorphisms. According to well-known results of Szekeres and Kopell, Z1 is a one-parameter group. On the other hand, Sergeraert constructed an f whose centralizer Zr, 2 r ∞, reduces to the group generated by f. We show that Zr can actually be a proper dense and uncountable subgroup of Z1 and that this phenomenon is not scarce.
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