2012/11/21 by Tom Kempton, Kempton, Tom
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Advanced Mathematical Theories and Applications #History and Theory of Mathematics
paper · pdf · doi:10.48550/arxiv.1211.5023
It is well known that the Bernoulli convolution νβ associated to the golden mean has Hausdorff dimension less than 1, i.e. that there exists a set A with νβ(A)=1 and dimH(A)<1. We construct such a set A explicitly and discuss how our approach might be generalised to prove the singularity of other Bernoulli convolutions