Mellin transforms of correlation integrals and generalized dimension of strange sets.

摘要: The Mellin transform of the correlation integral is introduced and proved to be equal energy whose divergence abscissa a lower bound Hausdorff dimension. For some Julia sets exact results are obtained. linear Cantor on real axis it shown that meromorphic, pole, determining abscissa, has sequence satellite poles equally spaced line parallel imaginary axis, which explain oscillations observed in numerical calculations integral. order-d generalized integrals as transforms for they have same singularities ordinary integrals. Letting ${r}_{d}$ residue pole corresponding ${\mathrm{lim}}_{\mathrm{d}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$(-${\mathrm{d}}^{\mathrm{\ensuremath{-}}1}$ln${r}_{d}$) second Renyi entropy. Some obtained discussed.