An Improved Result for Positive Measure Reducibility of Quasi-periodic Linear Systems

Abstract

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: Ẋ = (A(λ) + F(ϕ, λ))X, \( \dot{\varphi } = \omega \)where the parameter λ ∈ (a, b), ω is a fixed Diophantine vector, which is a generalization of Jorba & Simo’s positive measure reducibility result.