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Archiv der Mathematik

, Volume 92, Issue 6, pp 614–625 | Cite as

Multifractal formalism for self-affine measures with overlaps

  • Qi-Rong Deng
  • Sze-Man Ngai
Article

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.

Mathematics Subject Classification (2000).

Primary 28A80 Secondary 28A78 

Keywords.

Self-affine measure multifractal formalism dimension spectrum Lq-spectrum iterated function system with overlaps asymptotic weak separation condition 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsFujian Normal UniversityFuzhouChina
  2. 2.Department of Mathematical SciencesGeorgia Southern UniversityStatesboroUSA

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