2002/05/01 by Ben Hambly, B. M. HAMBLY, JUN KIGAMI +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Mathematical Dynamics and Fractals #Theoretical and Computational Physics
paper · doi:10.1017/s0305004101005618
openalex publication_date 2002/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
We introduce the concepts of local spectral and walk dimension for fractals. For a class of finitely ramified fractals we show that, if the Laplace operator on the fractal is defined with respect to a multifractal measure, then both the local spectral and walk dimensions will have associated non-trivial multifractal spectra. The multifractal spectra for both dimensions can be calculated and are shown to be transformations of the original underlying multifractal spectrum for the measure, but with respect to the effective resistance metric.