Multifractal formalism for self-affine measures with overlaps
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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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