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.