AI 中文总结
本文针对受随时间衰减非自治扰动的低维各向同性法椭圆/双曲不变环面哈密顿系统，证明了扩展相空间不变流形存在性并确定横向动力学渐近行为，结果适用于Hölder、光滑及解析哈密顿系统。
AI 中文摘要
许多物理现象可由受随时间衰减的非自治扰动作用的动力系统建模，包括激光脉冲与分子的相互作用、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椭圆（或双曲）不变环面（含拟周期解）的哈密顿系统，其受随时间衰减的时变扰动作用。在扰动衰减速率合适的条件下，我们证明了扩展相空间中不变流形的存在性，并确定了相关横向动力学的渐近行为。上述结果适用于Hölder、光滑及解析哈密顿系统。
英文摘要
Many physical phenomena are naturally modeled by dynamical systems subject to non-autonomous perturbations that decay in time, including the interaction of a laser pulse with a molecule, epidemiological models, nonlinear oscillatory systems, and celestial mechanics. In the present paper, we consider time-dependent perturbations decaying in time of Hamiltonian systems having a lower-dimensional isotropic normally elliptic (resp. hyperbolic) invariant torus with quasiperiodic solutions. Under suitable rates of decay in time of the perturbation, 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.
