Heat conductivity in linear mixing systems

We present analytical and numerical results on the heat conduction in a linear mixing system. In particular we consider a quasi-one-dimensional channel with triangular scatterers with internal angles which are irrational multiples of pi, and we show that the system obeys the Fourier law of heat conduction. Therefore, deterministic diffusion and normal heat transport which are usually associated with full hyperbolicity, actually take place in systems without exponential instability.