Multifractal Formalism for Self-Affine Measures with Overlaps

Authors

Qi-Rong Deng, Fujian Normal UniversityFollow
Sze-Man Ngai, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

6-2009

Publication Title

Archiv der Mathematik

DOI

10.1007/s00013-009-2969-9

ISSN

1420-8938

Abstract

We prove that for a class of self-affine measures defined by an expanding matrix whose eigenvalues have the same modulus, the L ^q-spectrum τ(q) is differentiable for all q > 0. Furthermore, we prove that the multifractal formalism holds in the region corresponding to q > 0.

Recommended Citation

Deng, Qi-Rong, Sze-Man Ngai. 2009. "Multifractal Formalism for Self-Affine Measures with Overlaps." Archiv der Mathematik, 92 (6): 514-625. doi: 10.1007/s00013-009-2969-9
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/122