Local dimensions for the random beta-transformation

Published 2 Nov 2012 in math.DS | (1211.0454v1)

Abstract: The random beta-transformation K is isomorphic to a full shift. This relation gives an invariant measure for K that yields the Bernoulli convolution by projection. We study the local dimension of the invariant measure for K for special values of beta and use the projection to obtain results on the local dimension of the Bernoulli convolution.

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