On the centralizer of diffeomorphisms of the half-line

  • Hélène Eynard

    Université de Lyon, Lyon, France


Let ff be a smooth diffeomorphism of the half-line fixing only the origin and ZrZ^r its centralizer in the group of CrC^r diffeomorphisms. According to well-known results of Szekeres and Kopell, Z1Z^1 is a one-parameter group. On the other hand, Sergeraert constructed an ff whose centralizer ZrZ^r, 2r2\le r\le \infty, reduces to the infinite cyclic group generated by ff. We show that ZrZ^r can actually be a proper dense and uncountable subgroup of Z1Z^1 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. 415–435

DOI 10.4171/CMH/229