Centralisateurs des difféomorphismes de la demi-droite

Abstract

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 ∞ reduces to the infinite cyclic group generated by f. We present here the main result of [3]: 𝒵 ∞ can actually be a proper and uncountable (hence dense) subgroup of 𝒵 1 .