I will discuss Hausdorff (fractal) dimension of limit Julia sets arising when iterating complex polynomials or rational functions on the Riemann sphere.

Methods used, belong to the thermodynamic formalism involving Kolmogorov entropy, Lyapunov exponents and geometric pressure and equilibria. A relation with the boundary behavior of conformal maps on the unit disc will be mentioned.

Prof. Feliks Przytycki is a Polish mathematician working on dynamical systems, ergodic theory, complex analysis. Prof. Pyzytycki currently works at the Institute of Mathematics  of Polish Academy of Sciences (IMPAN, Poland). He is member of Polish Academy of Sciences. He was invited speaker at the International Congress of Mathematicians 2018. During 2003-2016, he was the Deputy chairman of the Mathematics Committee of the Polish Academy and Chairman of the Polish National Committee for the International Mathematical Union.