Effective reducibility of a class of linear differential equations with quasiperiodic coefficients (Q1882499)

The authors consider the effective reducibility of the linear differential equation \[ \dot x= (A+ Q(t, \varepsilon))x,\quad |\varepsilon|\leq\varepsilon_0, \] where \(A\) is a constant matrix, \(Q(t,\varepsilon)\) is quasiperiodic in \(t\), and \(\varepsilon\) is a small perturbation parameter. In fact, they consider the more general case, which embraces both the multiple eigenvalues case and the degenerate case, and prove a similar result to that due to \textit{À. Jorba}, \textit{R. Ramírez-Ros} and \textit{J. Villanueva} [SIAM J. Math. Anal. 28, No. 1, 178--188 (1997; Zbl 0866.34032)].