A KAM theorem for Hamiltonian networks with long ranged couplings
A KAM theorem for Hamiltonian networks with long ranged couplings
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DOI：
10.1088/0951-7715/20/6/001
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发表时间：
2007-04
期刊：
影响因子：
1.7
通讯作者：
J. Geng;Y. Yi
中科院分区：
文献类型：
--
作者：
J. Geng;Y. Yi
我们考虑具有可变频率的长程弱耦合振子的哈密顿网络。通过导出一个抽象的无穷维KAM型定理，证明了对于任意给定的正整数N和N个可变频率的固定正测度集，存在一个正测度子集使得每个正测度子集对应于一个小振幅，准周期呼吸子（即在时间上是准周期性的，在空间上是指数局部化的解），频率从ω稍微变形。
We consider Hamiltonian networks of long-ranged and weakly coupled oscillators with variable frequencies. By deriving an abstract infinite dimensional KAM type of theorem, we show that for any given positive integer N and a fixed, positive measure set of N variable frequencies, there is a subset of positive measure such that each corresponds to a small amplitude, quasi-periodic breather (i.e. a solution which is quasi-periodic in time and exponentially localized in space) of the Hamiltonian network with N-frequencies which are slightly deformed from ω.