AI 中文总结
本文针对受多项式衰减时变扰动的低维各向同性法向抛物不变环面哈密顿系统，证明扩展相空间中不变流形存在性并确定横向动力学渐近行为，结果适用于多类哈密顿系统。
AI 中文摘要
受时间衰减非自治扰动作用的动力系统自然出现在诸多物理场景中，包括激光-分子相互作用、流行病学模型、非线性振荡系统及天体力学。本文研究具有低维各向同性法向抛物不变环面（支撑拟周期解）的哈密顿系统，其受多项式快速衰减的时变扰动，证明扩展相空间中不变流形的存在性，并确定相关横向动力学的渐近行为，上述结果对Hölder、光滑及解析哈密顿系统均成立。
英文摘要
Dynamical systems subject to non-autonomous perturbations decaying in time arise naturally in many physical contexts, including laser-molecule interactions, epidemiological models, nonlinear oscillatory systems, and celestial mechanics. In this paper, we consider time-dependent perturbations decaying polynomially fast in time of Hamiltonian systems having a lower-dimensional isotropic normally parabolic invariant torus supporting quasiperiodic solutions. We prove the existence of invariant manifolds in the extended phase space, and determine the asymptotic behavior of the associated transverse dynamics. The above results are obtained for Hölder, smooth, and analytic Hamiltonian systems.
