Hilbert′s Projective Metric on Cones of Dirichlet Forms

The construction of diffusions on finitely ramified fractals is straightforward if a certain nonlinear eigenvalue problem can be solved. Usually this problem is attacked probabilistically using Brouwer′s fixed point theorem. We will translate this problem into the theory of Dirichlet forms and apply a different fixed point approach, Hilbert′s projective metric on cones. This allows one to prove new results about the eigenvalue problem, especially about the uniqueness and the approximation of solutions, and about the structure of fixed point sets.