AVERAGING OF TIME{PERIODIC SYSTEMS WITHOUT A SMALL PARAMETER
AVERAGING OF TIME{PERIODIC SYSTEMS WITHOUT A SMALL PARAMETER
复制标题
没有小参数的时间{周期系统的平均
DOI：
10.3934/dcds.2006.14.753
复制
发表时间：
2010
影响因子：
1.1
通讯作者：
F. Varadi
中科院分区：
文献类型：
--
作者：
M. Chekroun;M. Ghil;Jean Roux;F. Varadi
在这篇文章中，我们提出了一种新的方法，平均在非哈密顿系统与周期强迫。这里的结果不依赖于小参数的存在。实际上，我们证明了我们的平均方法可以转化为一个适当的非线性等价问题，并且这个问题可以通过使用Lie变换框架线性化来形式化地解决，根据这种方法，我们导出了与一阶和高阶平均相关的形式坐标变换，从而得到了比经典公式更易于处理的公式。利用这些变换，可以通过恢复原始非平均系统的振荡分量来校正平均系统的解。在这个框架中，逆变换也明确定义的正式系列，他们允许估计适当的初始数据为每个高阶平均系统，尊重等价关系。最后，我们展示了如何使用这些方法来识别和计算一个非常大的一类非线性系统的时间周期强迫的周期解。我们测试我们的方法的有效性，通过分析一阶和二阶平均系统在大气化学中的一个问题。
In this article, we present a new approach to averaging in non- Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In fact, we show that our averaging method flts into an appropriate nonlinear equivalence problem, and that this problem can be solved formally by using the Lie transform framework to linearize it. According to this approach, we derive formal coordinate transformations asso- ciated with both flrst-order and higher-order averaging, which result in more manageable formulae than the classical ones. Using these transformations, it is possible to correct the solution of an averaged system by recovering the oscillatory components of the original non- averaged system. In this framework, the inverse transformations are also de- flned explicitly by formal series; they allow the estimation of appropriate initial data for each higher-order averaged system, respecting the equivalence rela- tion. Finally, we show how these methods can be used for identifying and com- puting periodic solutions for a very large class of nonlinear systems with time- periodic forcing. We test the validity of our approach by analyzing both the flrst-order and the second-order averaged system for a problem in atmospheric chemistry.