论文标题
鞍形中心和周期性轨道：在对称异质连接附近的动力学
Saddle-center and periodic orbit: dynamics near symmetric heteroclinic connection
论文作者
论文摘要
在其对称的杂智性连接的邻里研究了一个具有两种自由度的分析可逆的哈密顿系统，由对称的鞍形中心组成，一个对称定位的鞍形轨道，位于同一水平的哈密顿和两个非对称的杂斜球体中，并被引入了两个非对称的杂音轨迹。这是一个编构态的结构，因此可以在可逆的哈密顿系统的单参数家族中进行普遍满足。存在两种可能的这种连接，依赖于对均衡的反应的作用。 We prove a series of theorems which show a chaotic behavior of the system and those in its unfoldings, in particular, the existence of countable sets of transverse homoclinic orbits to the saddle periodic orbit in the critical level, transverse heteroclinic connections involving a pair of saddle periodic orbits, families of elliptic periodic orbits, homoclinic tangencies, families of homoclinic orbits to saddle-centers作为副产品，在展开等中，我们获得了鞍形中心的同型轨道轨道的标准。
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same level of a Hamiltonian and two non-symmetric heteroclinic orbits permuted by the involution. This is a codimension one structure and therefore it can be met generally in one-parameter families of reversible Hamiltonian systems. There exist two possible types of such connections in dependence on how the involution acts near the equilibrium. We prove a series of theorems which show a chaotic behavior of the system and those in its unfoldings, in particular, the existence of countable sets of transverse homoclinic orbits to the saddle periodic orbit in the critical level, transverse heteroclinic connections involving a pair of saddle periodic orbits, families of elliptic periodic orbits, homoclinic tangencies, families of homoclinic orbits to saddle-centers in the unfolding, etc. As a byproduct, we get a criterion of the existence of homoclinic orbits to a saddle-center.
