Differentiability of the Lq-spectrum and Multifractal decomposition by using infinite graph-directed IFSs

Guotai Deng Central China Normal University Sze-Man Ngai Hunan Normal University and Georgia Southern University

Dynamical Systems mathscidoc:1701.11001

By constructing an infinite graph-directed iterated iterated function system associated with a finite iterated function system, we develop a new approach for proving the differentiability of the $L^q$-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.
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@inproceedings{guotaidifferentiability,
  title={Differentiability of the Lq-spectrum and Multifractal decomposition by using infinite graph-directed IFSs},
  author={Guotai Deng, and Sze-Man Ngai},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170107175811939321709},
}
Guotai Deng, and Sze-Man Ngai. Differentiability of the Lq-spectrum and Multifractal decomposition by using infinite graph-directed IFSs. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170107175811939321709.
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