Reducibility Of 3-Dimensional Linear Quasi-periodic Systems With The Skew-symmetric Structure

In this paper we consider the reducibility of a class of 3-dimensional linear real analytic quasi-periodic systems with the skew-symmetric structure under small perturbations. That is, consider the following system where A is a constant matrix and Q is an analytic quasi-periodic matrix with a small parameter e. Let A and Q be skew-symmetric matrices. We will mainly use the method of KAM iteration to prove that under some non-resonance conditions about the frequencies of quasi-periodic system and eigenvalues of A, without any assumption of non-degeneracy conditions, the system is reducible for most sufficiently small parameters.