2021/02/15 by Tom Kempton, Kempton, Tom, Alex Batsis +1
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Analytic Number Theory Research #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2102.07581
Given a real number beta > 1, the spectrum of beta is a well studied dynamical object. In this article we show the existence of a certain measure on the spectrum of beta related to the distribution of random polynomials in beta, and discuss the local structure of this measure. We also make links with the question of the Hausdorff dimension of the corresponding Bernoulli Convolution