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ArticleOriginal scientific text

Title

Lq-spectrum of the Bernoulli convolution associated with the golden ratio

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
  2. Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
  3. Department of Mathematics, Cornell University, Ithaca, New York 14853 U.S.A.

Abstract

Based on a set of higher order self-similar identities for the Bernoulli convolution measure for (√5-1)/2 given by Strichartz et al., we derive a formula for the Lq-spectrum, q >0, of the measure. This formula is the first obtained in the case where the open set condition does not hold.

Keywords

ENG
Bernoulli convolution, golden ratio, multifractal measure, Lq-spectrum, Lq-dimension, Hausdorff dimension, renewal equation, self-similarity

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Studia Mathematica
1998/131/3
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Pages:
225-251
Main language of publication
English
Received
1997-07-16
Accepted
1998-04-15
Published
1998
Exact and natural sciences