Abstract
Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum. The asymptotic behavior of the eigenvalue counting function for the associated Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.
Original language | American English |
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State | Published - Sep 14 2016 |
Event | Harvard University Center of Mathematical Sciences and Applications Colloquium (CMSA) - Duration: Sep 14 2016 → … |
Conference
Conference | Harvard University Center of Mathematical Sciences and Applications Colloquium (CMSA) |
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Period | 09/14/16 → … |
Disciplines
- Mathematics
- Physical Sciences and Mathematics
Keywords
- Multifractal formalism
- Overlaps
- Self-similar measures
- Spectral asymptotics