Area distortion of quasiconformal mappings

In recent years quasiconformal mappings have been an efficient tool in the study of dynamical systems of the complex plane. We show here that, in turn, methods or ideas from dynamical systems can be used to solve a number of open questions in the theory of planar quasiconformal mappings. It has been known since the work of Ahlfors [A] and Mori [Mo] that K-quasiconformal mappings are locally H51der continuous with exponent 1/K. The function