Differentiability of L^q-Spectrum and Multifractal Decomposition by Using Infinite Graph-Directed IFSs

Authors

Guotai Deng, Central China Normal UniversityFollow
Sze-Man Ngai, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

4-30-2017

Publication Title

Advances in Mathematics

DOI

10.1016/j.aim.2017.02.021

ISSN

0001-8708

Abstract

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 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.

Recommended Citation

Deng, Guotai, Sze-Man Ngai. 2017. "Differentiability of L^q-Spectrum and Multifractal Decomposition by Using Infinite Graph-Directed IFSs." Advances in Mathematics, 311: 190-237. doi: 10.1016/j.aim.2017.02.021
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/649