A centre theorem for two-dimensional complex holomorphic systems and its generalization
A centre theorem for two-dimensional complex holomorphic systems and its generalization
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DOI：
10.1098/rspa.1995.0082
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发表时间：
1995-08
期刊：
影响因子：
--
通讯作者：
D. Needham
中科院分区：
文献类型：
--
作者：
D. Needham
我们考虑一个二维复全纯系统。特别地，我们将中心流形理论与C. H.布里奥特和J. C. Bouquet（J.小息肉21，133（1856））建立了一个中心定理，该定理涉及系统在具有单个纯虚本征值的平衡点附近的相路径的行为。对于相应的N维复全纯系统（N ≥ 3），建立了一个推广的中心定理.
We consider a two-dimensional complex holomorphic system. In particular, we use the centre manifold theory together with the singular point theory of C. H. Briot & J. C. Bouquet (J. Éc. imp. Polyt. 21, 133 (1856)) to establish a centre theorem concerning the behaviour of the phase paths of the system in the neighbourhood of an equilibrium point having a single purely imaginary eigenvalue. An extended centre theorem is established for the corresponding N-dimensional complex holomorphic system (N ≥ 3).