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

Copyright

This work is archived and distributed under the repository's Standard Copyright and Reuse License (opens in new tab). End users may copy, store, and distribute this work without restriction. For all other uses, permission must be obtained from the copyright owners or their authorized agents.