Centre families in two-dimensional complex holomorphic dynamical systems

被引：4

作者：

Needham, DJ ^{[1
]}

McAllister, S ^{[1
]}

机构：

[1] Univ Reading, Dept Math, Reading RG6 6AX, Berks, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1998年 / 454卷 / 1976期

关键词：

dynamical systems; holomorphic; centre families;

D O I：

10.1098/rspa.1998.0258

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：2267 / 2278

页数：12

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