Resumen de On the centralizer of diffeomorphisms of the half-line

Hélène Eynard

• 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 infinite cyclic 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.