On the Hausdorff Dimension of Bernoulli Convolutions
Akiyama, Shigeki · Feng, De-Jun · Kempton, Tom · Persson, Tomas
Original · EN
We give an expression for the Garsia entropy of Bernoulli convolutions in terms of products of matrices. This gives an explicit rate of convergence of the Garsia entropy and shows that one can calculate the Hausdorff dimension of the Bernoulli convolution νβ to arbitrary given accuracy whenever β is algebraic. In particular, if the Garsia entropy H(β) is not equal to (β) then we have a finite time algorithm to determine whether or not dimₕ (νβ)=1.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.