Intrinsic irreversibility and the validity of the kinetic description of chaotic systems

Irreversibility for a class of chaotic systems is seen to be an exact consequence of the dynamics through the use of a generalized spectral representation of the time evolution operator of probability densities. The generalized representation is valid for one-dimensional systems when the initial probability density satisfies certain ''physical conditions'' of smoothness. The formalism is first applied to the one-dimensional multi-Bernoulli map, which is a simple map displaying deterministic diffusion. The two-dimensional, invertible baker and multibaker transformations are then studied and the physical conditions determining which discrete spectral values are realized are seen to depend on the smoothness of both the density as well as the observable considered. The generalized representation is constructed using a resolvent formalism. The eigenstates of the diffusive systems are seen to be of a fractal nature