Occurrence of periodic Lame functions at bifurcations in chaotic Hamiltonian systems
Occurrence of periodic Lame functions at bifurcations in chaotic Hamiltonian systems
复制标题
混沌哈密顿系统分岔处周期性拉梅函数的出现
DOI：
10.1088/0305-4470/34/40/301
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Kaori Tanaka
中科院分区：
文献类型：
--
作者：
M. Brack;Mitaxi Mehta;Kaori Tanaka;Kaori Tanaka
本文研究了混合相空间中二维哈密顿系统的直线振动轨道的等熵分叉级联。我们表明，新的分叉轨道，这是负责的发病混沌，解析给出的周期解的拉梅方程分类在1940年的因斯。在具有C2v对称性的哈密尔顿算符中，它们分别交替出现为周期为2K和4K的拉梅函数，其中4K是拉梅方程中出现的雅可比椭圆函数的周期。我们还表明，在岛链型倍周期分岔产生的两对轨道给出了两个不同的线性组合的代数拉梅函数与周期8K。
We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lame equation as classified in 1940 by Ince. In Hamiltonians with C2v symmetry, they occur alternatingly as Lame functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lame equation. We also show that the two pairs of orbits created at period-doubling bifurcations of island-chain type are given by two different linear combinations of algebraic Lame functions with period 8K.