  Consider an infinite tree. A hierarchomorphism (spheromorphism) is a
homeomorphism of the absolute which can be extended to the tree except a finite
subtree. Examples of groups of hierarchomorphisms: groups of locally analitic
diffeomorphisms of $p$-adic line; also Richard Thompson groups. The groups of
hierarchomorphisms have some properties similar to the group of diffeomorphisms
of the circle. We discuss actions of groups of ierarchomorphisms in some
natural Hilbert spaces associated with trees.
