The gluing bifurcation: I. Symbolic dynamics of the closed curves
The gluing bifurcation: I. Symbolic dynamics of the closed curves
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DOI：
10.1088/0951-7715/1/1/008
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发表时间：
1988-02-01
期刊：
影响因子：
1.7
通讯作者：
Tresser, C.
中科院分区：
文献类型：
--
作者：
Gambaudo, J. M.;Glendinning, P.;Tresser, C.
本文研究了余维二胶合分岔的周期轨道，该分岔涉及两条双渐近于同一驻点的轨道。只要满足一些简单的条件，我们就证明了存在零条、一条或两条闭曲线，并且这些闭曲线霍韦特定的符号形式，特别是，它允许我们将它们中的每一条曲线与一个旋转数联系起来。此外，可以共存的轨道对被确定：两个旋转数必须是Farey邻居。
We study the periodic orbits which can occur in a neighbourhood of a codimension-two gluing bifurcation involving two trajectories bi-asymptotic to the same stationary point. Provided some simple conditions are satisfied we prove that there are either zero, one or two closed curves and that these hove a specific symbolic form which, in particular, allows us to associate a rotation number with each of them. Furthermore, pairs of orbits which can coexist are identified: the two rotation numbers must be Farey neighbours.