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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: $$\dot x= Ax+f(t,x,\varepsilon),\quad x\in\Bbb R^2$$ 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 $\varepsilon$.

34C20Transformation and reduction of ODE and systems, normal forms
Full Text: DOI
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