# American Institute of Mathematical Sciences

January  2016, 36(1): 345-360. doi: 10.3934/dcds.2016.36.345

## Polynomial and linearized normal forms for almost periodic differential systems

 1 School of Mathematics, Peking University, Beijing 100871 2 Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia 3 Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China

Received  October 2013 Revised  May 2014 Published  June 2015

For almost periodic differential systems $\dot x= \varepsilon f(x,t,\varepsilon)$ with $x\in \mathbb{C}^n$, $t\in \mathbb{R}$ and $\varepsilon>0$ small enough, we get a polynomial normal form in a neighborhood of a hyperbolic singular point of the system $\dot x= \varepsilon \lim_{T \to \infty} \frac {1} {T} \int_0^T f(x,t,0) dt$, if its eigenvalues are in the Poincaré domain. The normal form linearizes if the real part of the eigenvalues are non--resonant.
Citation: Weigu Li, Jaume Llibre, Hao Wu. Polynomial and linearized normal forms for almost periodic differential systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 345-360. doi: 10.3934/dcds.2016.36.345
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