Dynamical stability of quasi-periodic response solutions in planar conservative systems
Dynamical stability of quasi-periodic response solutions in planar conservative systems
复制标题
平面保守系统准周期响应解的动态稳定性
DOI：
10.1016/j.indag.2012.01.001
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
C. Simó
中科院分区：
文献类型：
--
作者：
H. Hanßmann;C. Simó
我们研究了在原点消失的非自治平面哈密顿向量场或可逆向量场。时间依赖是准周期的，具有强烈的非谐振频率。首先，我们用平均系统的形式给出了平凡解是动态稳定的一个简单准则。然后，我们得到了不满足判据条件的一类例子的不稳定性。最后给出了用平均为零的向量场来稳定不稳定平凡解的可能方法。
We study non-autonomous planar Hamiltonian or reversible vector fields that vanish at the origin. The time-dependence is quasi-periodic with strongly non-resonant frequencies. First, we give a simple criterion in terms of the averaged system for the trivial solution to be dynamically stable. Then we obtain destabilizations for classes of examples where the conditions of the criterion are not satisfied. We end with possible ways to stabilize an unstable trivial solution by means of vector fields with zero average.