On the centralizer of diffeomorphisms of the half-line
Abstract
Description
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.
16 pages, 5 figures
16 pages, 5 figures