Analysis of positive measure reducibility for quasi-periodic linear systems under Brjuno-Rüssmann condition

Abstract

<abstract><p>In this article, we discuss the positive measure reducibility for quasi-periodic linear systems close to a constant which is defined as:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \frac{dx}{dt} = (A(\lambda) + Q(\varphi,\lambda))x, \dot{\varphi} = \omega, \end{align*} $\end{document} </tex-math></disp-formula></p> <p>where $ \omega $ is a Brjuno vector and parameter $ \lambda\in (a, b) $. The result is proved by using the KAM method, Brjuno-Rüssmann condition, and non-degeneracy condition.</p></abstract>