Computing Garsia Entropy for Bernoulli Convolutions with Algebraic Parameters

Abstract

We introduce a parameter space containing all algebraic integers $\beta \in (1,2]$ that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the Garsia entropy of the Bernoulli convolution ${\nu }_{\beta }$. This allows us to show that ${\dim }_{\mathrm{H}}({\nu }_{\beta })=1$ for all $\beta$ with representations in certain open regions of the parameter space.

Withdrawn due to coauthor disagreement

References in corpus (1)

• A lower bound for the dimension of Bernoulli convolutions

Cited by in corpus (2)

• Estimates on the dimension of self-similar measures with overlaps
• Measures on the Spectra of Algebraic Integers