Mirko Degli Esposti, Stefano Isola
Distribution of periodic orbits for linear automorphisms of tori.
(41K, Plain-Tex)

ABSTRACT.  In this paper we study the distribution properties 
of periodic orbits for the linear hyperbolic automorphisms 
of the $d$-torus. We first obtain an explicit expression 
of the dynamical zeta function and prove general equidistribution 
results similar to those obtained for Axiom A flows.  
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 theoretic exponential sum over 
a finite field. This fact enables us to obtain explicit 
estimates on their asymptotic distributional properties.