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首页> 外文期刊>Annales de l'Institut Fourier >Smooth gevrey normal forms of vector fields near a fixed point
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Smooth gevrey normal forms of vector fields near a fixed point

机译：Smooth gevrey normal forms of vector fields near a fixed point

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摘要

We study germs of smooth vector fields in a neighborhood of a fixed point having an hyperbolic linear part at this point. It is well known that the "small divisors" are invisible either for the smooth linearization or normal form problem. We prove that this is completely different in the smooth Gevrey category. We prove that a germ of smooth α-Gevrey vector field with an hyperbolic linear part admits a smooth β-Gevrey transformation to a smooth β-Gevrey normal form. The Gevrey order β depends on the rate of accumulation to 0 of the small divisors. We show that a formally linearizable smooth Gevrey germ with the linear part satisfying Brjuno's small divisors condition can be linearized in the same Gevrey class.

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