Let be a smooth diffeomorphism of the half-line fixing only the origin and its centralizer in the group of diffeomorphisms. According to well-known results of Szekeres and Kopell, is a one-parameter group. On the other hand, Sergeraert constructed an whose centralizer , , reduces to the infinite cyclic group generated by . We show that can actually be a proper dense and uncountable subgroup of and that this phenomenon is not scarce.
Cite this article
Hélène Eynard, On the centralizer of diffeomorphisms of the half-line. Comment. Math. Helv. 86 (2011), no. 2, pp. 415–435DOI 10.4171/CMH/229