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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:
$\dot x= Ax+f(t,x,\varepsilon),\quad x\in\mathbb R^2$
where $$A$$ is a real $$2\times 2$$ constant matrix, and $$f(t,0,\varepsilon)=O(\varepsilon)$$ and $$\partial_xf(t,0,\varepsilon)=O(\varepsilon)$$ as $$\varepsilon\to 0$$. With some nonresonant conditions of the frequencies with the eigenvalues of $$A$$ and without any nondegeneracy condition with respect to $$\varepsilon$$, by an affine analytic quasiperiodic transformation we change the system to a suitable normal form at the zero equilibrium for sufficiently small perturbation parameter $$\varepsilon$$.

##### MSC:
 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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##### References:
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