#### Title

The Multifractal Formalism and Spectral Asymptotics of Self-Similar Measures With Overlaps

#### Document Type

Presentation

#### Publication Date

9-14-2016

#### 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.

#### Sponsorship/Conference/Institution

Harvard University Center of Mathematical Sciences and Applications Colloquium (CMSA)

#### Location

Cambridge, MA

#### Recommended Citation

Ngai, Sze-Man.
2016.
"The Multifractal Formalism and Spectral Asymptotics of Self-Similar Measures With Overlaps."
*Mathematical Sciences Faculty Presentations*.
Presentation 18.

https://digitalcommons.georgiasouthern.edu/math-sci-facpres/18