论文标题
同质轨道的不变流形和超智能的动态后果：（mathbb {r}^4）中的案例研究（Mathbb {z} _2） - 运动的积分和积分
Invariant manifolds of homoclinic orbits and the dynamical consequences of a super-homoclinic: A case study in (mathbb{R}^4) with (mathbb{Z}_2)-symmetry and integral of motion
论文作者
论文摘要
我们考虑（Mathbb {Z} _2） - 具有运动积分和具有横向同质轨道（gamma）的双曲线平衡的（Mathbb {r}^{4}）中的（Mathbb {r}^{4}）中的（Mathbb {Z} _2） - 等级流。我们提供了（伽玛）稳定且不稳定的不变流形的标准。我们证明，如果这些歧管横向相交，创建了所谓的超级智能，那么在这种超智慧的任何社区中，都存在无限的多个多脉冲同层循环。考虑了耦合非线性schrödinger方程系统的应用。
We consider a (mathbb{Z}_2)-equivariant flow in (mathbb{R}^{4}) with an integral of motion and a hyperbolic equilibrium with a transverse homoclinic orbit (Gamma). We provide criteria for the existence of stable and unstable invariant manifolds of (Gamma). We prove that if these manifolds intersect transversely, creating a so-called super-homoclinic, then in any neighborhood of this super-homoclinic there exist infinitely many multi-pulse homoclinic loops. An application to a system of coupled nonlinear Schrödinger equations is considered.
