FROM DYNAMICAL CHAOS TO DIFFUSION

We briefly review several recent results in the theory of diffusion in the light of the last decade advances on dynamical systems. We show how the diffusion coefficient can be calculated from the classical Ruelle resonances of the dynamical system, i.e., from complex zeros of the dynamical zeta function. The diffusion coefficient is also related to the characteristic properties of chaos on the fractal repeller underlying the diffusion process in open deterministic systems. Finally, we present a thermodynamic formalism based on the generating function of the diffusion coefficient and higher moments of diffusion and we show how anomalous diffusion is related to dynamical phase transitions in this formalism.