On the reducibility of a class of nonlinear quasi-periodic system with small perturbation parameter near zero equilibrium point

摘要

This work focuses on the reducibility of the following real nonlinear analytical quasiperiodic system: (x)over dot = Ax + f (t, x, epsilon), x is an element of R-2 where A is a real 2 x 2 constant matrix, and f(t, 0, epsilon) = O(epsilon) and partial derivative x f (t, 0, epsilon) = O(epsilon) as epsilon --> 0. With some non-resonant conditions of the frequencies with the eigenvalues of A and without any nondegeneracy condition with respect to epsilon, by an affine analytic quasiperiodic transformation we change the system to a suitable norm form at the zero equilibrium for most of the sufficiently small perturbation parameter epsilon. (C) 2007 Elsevier Ltd. All rights reserved.