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On the reducibility of a class of nonlinear quasi-periodic system with small perturbation parameter near zero equilibrium point. (English) Zbl 1151.34030

Summary: This work focuses on the reducibility of the following real nonlinear analytical quasiperiodic system:

x ˙=Ax+f(t,x,ε),x 2

where A is a real 2×2 constant matrix, and f(t,0,ε)=O(ε) and x f(t,0,ε)=O(ε) as ε0. With some nonresonant conditions of the frequencies with the eigenvalues of A and without any nondegeneracy condition with respect to ε, by an affine analytic quasiperiodic transformation we change the system to a suitable normal form at the zero equilibrium for sufficiently small perturbation parameter ε.

34C20Transformation and reduction of ODE and systems, normal forms