An improved result for positive measure reducibility of quasi-periodic linear systems

In this paper, by the KAM method, under weaker small denominator conditions and nondegeneracy conditions, we prove a positive measure reducibility for quasi-periodic linear systems close to constant: X = (A(lambda) + F(rho, lambda))X, (rho)over dot = omega where the parameter lambda is an element of (a, b), omega is a fixed Diophantine vector, which is a generalization of Jorba & Simo's positive measure reducibility result.