报告摘要：The study of diffusion processes on fractals emerged as an independent research field in the late $80$'s. For p.c.f. self-similar sets Kigami showed that Dirichlet forms can be constructed as limits of electrical networks on approximation graphs. The construction relies on determining a proper form on the initial graph, whose existence and uniqueness in general is a difficult and fundamental problem in fractal analysis. In this talk, we consider the problem for three classes of fractals: 1. the Julia sets of Misiurewicz-Sierpinski maps; 2. the Sierpinski gasket with added rotational triangle; 3. the golden ratio Sierpinski gasket. The first ones come from complex dynamics which are not strictly self-similar sets. The second ones are due to Barlow which are not p.c.f. in general. The third one is a typical example which satisfies a graph-directed construction, but is not finitely ramified.