Morse decomposition of global attractors with infinite components
Morse decomposition of global attractors with infinite components
复制标题
DOI：
10.3934/dcds.2015.35.2845
复制
发表时间：
2015
影响因子：
1.1
通讯作者：
T. Caraballo;J. C. Jara;J. Langa;J. Valero
中科院分区：
文献类型：
--
作者：
T. Caraballo;J. C. Jara;J. Langa;J. Valero
本文讨论了具有可数集的莫尔斯分解的一些动力学性质。特别地，我们能够证明莫尔斯集合上的梯度动力学与分离假设等价于与莫尔斯集合相关的有序Lyapunov函数的存在性，也等价于莫尔斯分解的存在性——即，全局吸引子可以被描述为一个不断增加的局部吸引子族及其相关的排斥子族。
In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, we are able to prove that the gradient dynamics on Morse sets together with a separation assumption is equivalent to the existence of an ordered Lyapunov function associated to the Morse sets and also to the existence of a Morse decomposition -that is, the global attractor can be described as an increasing family of local attractors and their associated repellers.