Topology of optimal flows with collective dynamics on closed orientable surfaces
Topology of optimal flows with collective dynamics on closed orientable surfaces
复制标题
封闭可定向表面上具有集体动力学的最优流动拓扑
DOI：
10.15673/tmgc.v13i2.1731
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发表时间：
2020
影响因子：
--
通讯作者：
M. V. Loseva
中科院分区：
文献类型：
--
作者：
A. Prishlyak;M. V. Loseva
我们考虑一个封闭的表面上的流动与一个或多个异宿周期，分为两个区域的表面。其中一个区域具有梯度动力学，就像莫尔斯场。另一个区域具有由简单莫尔斯函数的斜梯度场产生的哈密顿动力学。我们利用Reeb图和Oshemkov-Shark图构造了流的完全拓扑不变量，并研究了它的性质。我们描述了所有可能的结构的最优流与集体动力学的面向表面的属不超过2，无论是流包含一个中心和流没有它。
We consider flows on a closed surface with one or more heteroclinic cycles that divide the surface into two regions. One of the region has gradient dynamics, like Morse fields. The other region has Hamiltonian dynamics generated by the field of the skew gradient of the simple Morse function. We construct the complete topological invariant of the flow using the Reeb and Oshemkov-Shark graphs and study its properties. We describe all possible structures of optimal flows with collective dynamics on oriented surfaces of genus no more than 2, both for flows containing a center and for flows without it.