Karoly Simon, BME Budapest

Title:
Hausdorff dimension for some non-Markovian repellers (joint with Bal\'azs B\'ar\'any and Michal Rams)

Abstract:

We combine techniques from one-dimensional dynamics and fractal geometry to compute the Hausdorff dimension of function graphs including generalized fractal interpolation functions and generalized Takagi functions.

The function graphs under consideration are repellers of some piecewise affine and piecewise expanding maps. In general, the underlying dynamics cannot be described by any subshift of finite type. This non-Markovian behaviour of the repellers under consideration is tackled by approximation by Markovian sub-systems, using a notion of the topological pressure introduced by Franz Hofbauer. 

Although the motivation of our research was to answer a fractal image compression related question asked by Michael Barnsley, during the talk, we do not need to know what fractal image compression is.