%0 Journal Article %1 hambly2002multifractal %A Hambly, B. M. %A Kigami, Jun %A Kumagai, Takashi %D 2002 %J Mathematical Proceedings of the Cambridge Philosophical Society %K Brownian_motion_on_fractals Hausdorff_dimension multifractal random_walk_dimension %N 03 %P 555--571 %R 10.1017/S0305004101005618 %T Multifractal formalisms for the local spectral and walk dimensions %U http://journals.cambridge.org/article_S0305004101005618 %V 132 %X ABSTRACT 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.

@article{hambly2002multifractal, abstract = { ABSTRACT 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. }, added-at = {2013-10-21T16:17:47.000+0200}, author = {Hambly, B. M. and Kigami, Jun and Kumagai, Takashi}, biburl = {https://www.bibsonomy.org/bibtex/2ea6aeda0006f5346555f966497dcdc18/peter.ralph}, doi = {10.1017/S0305004101005618}, interhash = {3839d5f1f4a0e563c9476d8a79ab852f}, intrahash = {ea6aeda0006f5346555f966497dcdc18}, issn = {1469-8064}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society}, keywords = {Brownian_motion_on_fractals Hausdorff_dimension multifractal random_walk_dimension}, month = {5}, number = 03, numpages = {17}, pages = {555--571}, timestamp = {2013-10-21T16:17:47.000+0200}, title = {Multifractal formalisms for the local spectral and walk dimensions}, url = {http://journals.cambridge.org/article_S0305004101005618}, volume = 132, year = 2002 }