Differentiability of Lq-Spectrum and Multifractal Decomposition by Using Infinite Graph-Directed IFSs
Advances in Mathematics
By constructing an infinite graph-directed iterated function system associated with a finite iterated function system, we develop a new approach for proving the differentiability of the Lq-spectrum and establishing the multifractal formalism of certain self-similar measures with overlaps, especially those defined by similitudes with different contraction ratios. We apply our technique to a well-known class of self-similar measures of generalized finite type.
Deng, Guotai, Sze-Man Ngai.
"Differentiability of Lq-Spectrum and Multifractal Decomposition by Using Infinite Graph-Directed IFSs."
Advances in Mathematics, 311: 190-237.