Spectral asymptotic of fractal lattices in problems of diagnostics of material fatigue

The inverse spectral problem on fractal lattices which deals with obtaining Minkovsky´s dimension from the spectrum of the boundary problem for the Laplace operator on fractal lattice was observed. We considered high-frequency asymptotic of spectral function this operator as a data of the inverse problem. Heat kernel method let us to use Monte-Carlo technique for obtaining fractal asymptotic of fractal lattices with different systems of iteration functions and boundary conditions. The results obtained in this paper give us the possibility of determining fractal dimension. Also given the connection between studying problem and the problem of determining material fatigue which has fractal parametrization.