论文标题
丰富的无限切换
Abundance of infinite switching
论文作者
论文摘要
在本文中，我们描述了一类表现出丰富开关的向量场}网络附近：对于网络的每个社区和每个无限允许的路径，遵循该路径的社区中的一组初始条件集具有正面的lebesgue度量。 The proof relies on the existence of "large'' strange attractors in the terminology of Broer, Simó and Tatjer (Nonlinearity, 667--770, 1998) near a heteroclinic tangle unfolding an attracting network with a two-dimensional heteroclinic connection. For our class of vector fields, any small non-empty open ball of initial conditions realizes infinite switching. We illustrate the theory with a specific一个参数的微分方程家族，为此，我们能够为其几乎所有参数表征其全局动力学。
In this article, we describe a class of vector fields exhibiting abundant switching} near a network: for every neighbourhood of the network and every infinite admissible path, the set of initial conditions within the neighbourhood that follows the path has positive Lebesgue measure. The proof relies on the existence of "large'' strange attractors in the terminology of Broer, Simó and Tatjer (Nonlinearity, 667--770, 1998) near a heteroclinic tangle unfolding an attracting network with a two-dimensional heteroclinic connection. For our class of vector fields, any small non-empty open ball of initial conditions realizes infinite switching. We illustrate the theory with a specific one-parameter family of differential equations, for which we are able to characterise its global dynamics for almost all parameters.
