Amplitudes from eigenvalues
Amplitudes from eigenvalues
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特征值的振幅
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
L. Tuckerman
中科院分区：
文献类型：
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作者：
L. Tuckerman
通常通过线性稳定性分析来理解动力系统，线性稳定性分析归结为矩阵的对角化，然后通过研究非线性项的影响来理解动力系统。令人惊讶的是，在许多感兴趣的情况下，非线性分析也可以简化为矩阵的对角化(类似于线性稳定矩阵)，其特征值产生非线性幅度。这为通常的余维展开--两点展开或动力系统对称性分类提供了一种补充选择。这种系统的例子可以在二元流体对流和圆柱对流或旋转对流中找到。
A dynamical system is generally understood first via linear stability analysis, which reduces to the diagonalization of a matrix, and then by studying the effects of the nonlinear terms. Surprisingly, in many cases of interest, the nonlinear analysis can also be reduced to the diagonalization of a matrix (similar to the linear stability matrix) whose eigenvalues yield nonlinear amplitudes. This provides a complementary alternative to the usual unfolding of codimension-two points or to the classification of dynamical systems by symmetry. Examples of such systems can be found in binary fluid convection and cylindrical or rotating convection.