论文标题
渐近汉密尔顿系统中的稳定性和分叉现象
Stability and bifurcation phenomena in asymptotically Hamiltonian systems
论文作者
论文摘要
考虑到时间依赖性扰动对中心类型平衡的自主哈密顿系统的影响。假定无穷大的扰动衰减在不受干扰的系统的平衡状态下消失。在这种情况下，轨迹的稳定性和长期行为取决于方程式的非线性和非自主术语。该论文研究了与平衡的Lyapunov稳定性的变化以及在渐近自主系统中的新吸引或排斥状态的出现有关的分叉。讨论了分叉对衰减扰动结构的依赖性。
The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the unperturbed system. In this case the stability and the long-term behaviour of trajectories depend on nonlinear and non-autonomous terms of the equations. The paper investigates bifurcations associated with a change of Lyapunov stability of the equilibrium and the emergence of new attracting or repelling states in the perturbed asymptotically autonomous system. The dependence of bifurcations on the structure of decaying perturbations is discussed.
