Title: Computation of the dimension of fractals.
Speaker: Mark Pollicott
Abstract: For many simple fractals there is no explicit expression for their dimension and it is only
possible to give numerical approximations. A simple example of this is the case of the set of numbers
in the real line whose continued fraction expansion takes digits from a finite given set of natural
numbers, and for which a precise knowledge is important in understanding the Lagrange spectrum in
diophantine approximation. Work of David Ruelle gave an implicit formula for the dimension of such
fractals and Curt McMullen showed how to use this expression to get good numerical estimates.
However, Jenkinson and I showed that a careful study of Ruelle's proof actually leads to a new
method of getting much more accurate numerical approximations to the true value.