The utility of an invariant manifold description of the evolution of a dynamical system
The utility of an invariant manifold description of the evolution of a dynamical system
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动力系统演化的不变流形描述的效用
DOI：
10.1137/0520094
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发表时间：
1989
影响因子：
2
通讯作者：
A. Roberts
中科院分区：
文献类型：
--
作者：
A. Roberts
一个物理系统的长期演化可能由少数几种模式所支配。一个不变的流形描述的渐近演化，简要讨论了两个简单的例子，可以给一个强大的和有用的观点的物理系统。不变流形和中心流形之间的关系也进行了讨论，因为是不变流形和模态数值逼近之间的关系。流体力学中的许多经典近似都可以看作是对近似不变流形上的演化的近似。
The long-time evolution of a physical system may be dominated by a small number of modes. An invariant manifold description of the asymptotic evolution, briefly discussed here in two simple examples, can give a powerful and useful view of the physical system. The relationship between invariant manifolds and centre manifolds is also discussed, as is the relationship between invariant manifolds and modal numerical approximations. Many classical approximations in fluid mechanics can be viewed as approximating the evolution on an approximate invariant manifold.