DISTRIBUTION OF CLOSED ORBITS FOR LINEAR AUTOMORPHISMS OF TORI

In this paper we study the distribution properties of periodic orbits for the linear hyperbolic automorphisms of the d-torus. We first obtai n an explicit expression of the dynamical zeta function and prove gene ral equidistribution results similar to those obtained for axiom A Row s. We then study in detail some families of periodic orbits living on invariant prime lattices: they have the property that the integral of any character along any single orbit can be reduced to a number theore tic exponential sum over a finite field. This fact enables us to obtai n explicit estimates on their asymptotic distributional properties.