ON THE REDUCIBILITY OF 2-DIMENSIONAL LINEAR QUASI-PERIODIC SYSTEMS WITH SMALL PARAMETERS.

In this paper we consider a real analytic linear quasi-periodic system of 2-dimension, whose coefficient matrix depends on a small parameter Cm-smoothly and closes to constant. Under some non-resonance conditions about the basic frequencies and the eigenvalues of the constant matrix and without any non-degeneracy assumption with respect to the small parameter, we prove that the system is reducible for many of the sufficiently small parameters. [ABSTRACT FROM AUTHOR]