The subgroup $PSL(2,R)$ is spherical in the group of diffeomorphisms of the circle

We show that the group $PSL(2,R)$ is a spherical subgroup in the group of $C^3$-diffeomorphisms of the circle. Also, the group of automorphisms of a Bruhat–Tits tree is a spherical subgroup in the group of hierarchomorphisms of the tree.