Invariant curves near Hamiltonian–Hopf bifurcations of four-dimensional symplectic maps
Invariant curves near Hamiltonian–Hopf bifurcations of four-dimensional symplectic maps
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四维辛映射哈密顿-霍普夫分岔附近的不变曲线
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
M. Ollé
中科院分区：
文献类型：
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作者：
À. Jorba;M. Ollé
在本文中，我们给出了辛映射不动点的扩展邻域的数值描述，该邻域经历了从线性稳定到复不稳定的无理转变，即所谓的哈密顿-霍普夫分岔。我们已经考虑了正向和逆向情况。本研究基于不动点附近李亚普诺夫族不变曲线的数值计算。我们展示了这些族如何与它们的不变流形和不动点的不变流形一起组织分叉周围的相空间。
In this paper, we give a numerical description of an extended neighbourhood of a fixed point of a symplectic map undergoing an irrational transition from linear stability to complex instability, i.e. the so-called Hamiltonian–Hopf bifurcation. We have considered both the direct and inverse cases.This study is based on numerical computation of the Lyapunov families of invariant curves near the fixed point. We show how these families, jointly with their invariant manifolds and the invariant manifolds of the fixed point, organize the phase space around the bifurcation.