Centre families in two–dimensional complex holomorphic dynamical systems
Centre families in two–dimensional complex holomorphic dynamical systems
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DOI：
10.1098/rspa.1998.0258
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发表时间：
1998-08
期刊：
影响因子：
--
通讯作者：
David Needham;S. McAllister
中科院分区：
文献类型：
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作者：
David Needham;S. McAllister
考虑一个二维复全纯动力系统。特别地，我们利用C. H. Briot和J.C. Bouquet建立存在的复杂的全纯不变流形的系统在附近的平衡点有两个纯虚特征值。因此，这使我们能够建立在平衡点附近的等值线中心家庭的存在。将所得结果应用于复杂的Takens-Bogdanov系统。
We consider a two–dimensional complex holomorphic dynamical system. In particular, we use the singular point theory of C. H. Briot and J. C. Bouquet to establish the existence of complex holomorphic invariant manifolds of the system in the neighbourhood of an equilibrium point with two purely imaginary eigenvalues. Consequently, this enables us to establish the existence of isochronous centre families in the neighbourhood of the equilibrium point. The results are exhibited by application to the complex Takens–Bogdanov system.