Kronecker's Diophantine Approximation and the Asymptotics of Solutions of Difference Equations

摘要

The asymptotic properties of the solutions of a class of linear, difference equations have been described-in increasing level of refinement-by many authors including H. Poincare, O. Perron, and, finally, M. Pituk. In this paper we provide a proof of the constantcoefficient case of Pituk's theorem based on the recurrence properties of rotations of the torus.