A p.c.f. self-similar set with no self-similar energy

Abstract

A general class of finitely ramified fractals is that of P.C.F. self-similar sets. An important open problem in analysis on fractals was whether there exists a self-similar energy on every P.C.F. self-similar set. In this paper, I solve the problem, showing an example of a P.C.F. self-similar set where there exists no self-similar energy.