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math.CA2004★ 22 cited
Overlapping self-affine sets
Pablo Shmerkin
We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, i…
math.CA2004
A Modified Multifractal Formalism for a Class of Self-Similar Measures
Pablo Shmerkin
The multifractal spectrum of a Borel measure in is defined as \[ f_μ(α) = \dim_H {x:\lim_{r\to 0} \frac{\log μ(B(x,r))}{\log r}=α}. \] For self-similar measures…