Analysis on Graphs and Fractals

Products of random matrices and derivatives on p.c.f. Fractals

A Pelander, Uppsala University, Sweden

Abstract

We define intrinsic first order derivatives on post critically finite fractals and prove a.e. differentiability with respect to self-similar measures for certain classes of fractals and functions. We apply our results to extend the geography is destiny principle to these cases. Our main tool is the Furstenberg-Kesten theory of products of random matrices. The talk is on joint work with A. Teplyaev