Center manifold approach to discrete integrable systems related to eigenvalues and singular values
Center manifold approach to discrete integrable systems related to eigenvalues and singular values
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DOI：
10.14492/hokmj/1272848032
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发表时间：
2007-11
影响因子：
0.5
通讯作者：
M. Iwasaki;Yoshimasa Nakamura
中科院分区：
文献类型：
--
作者：
M. Iwasaki;Yoshimasa Nakamura
中心流形的存在与动力系统的局部行为密切相关。在本文中，我们考虑离散 Toda 方程和离散 Lotka-Volterra 系统的中心流形。他们的解决方案收敛于某些结构化矩阵的特征值反奇异值。自由参数对于证明离散 Lotka-Volterra 系统中心流形的存在性起着关键作用。借助中心流形的存在性证明了离散Lotka-volterra系统解的单调收敛性。相反，离散 Toda 方程的中心流形并不总是存在。
The existence of center manifolds is closedly related to local behavior of dynamical systems. In this paper we consider center manifolds both of the discrete Toda equation and the discrete Lotka-Volterra system. Their solutions converge to eigenvalues anti singular values of certain structured matrices. A free parameter plays a key role to show the existence of a center manifold of the discrete Lotka-Volterra system. A monotone convergence of the solution of the discrete Lotka-volterra system is proved with the help of the existence of a center manifold. In contrast, a center manifold of the discrete Toda equation does not always exist.