论文标题
依赖时间依赖的哈密顿量的ic序列化解决方案
Biasymptotically quasiperiodic solutions for time-dependent Hamiltonians
论文作者
论文摘要
在先前的作品中，[渐近的二级溶液用于时间依赖性的汉密尔顿人，Arxiv预印型ARXIV：2211.06623（2022）]，我们考虑对汉密尔顿矢量场的时间依赖性扰动，具有支持quasiperiodicodic solutions的不变性圆环。假设扰动会随着时间的流逝而趋于多个金属，我们证明存在渐近kam圆环。渐近kam圆环是一个时间依赖的嵌入式摩ri的家族，因为时间倾向于无穷大于与不受干扰的系统相关的不变圆环。现在，很自然地想知道我们何时存在一个偏见的kam圆环。这是一个连续的时间依赖性的嵌入式托里（Tori）家族，并在未来和过去融合到合适的准静态不变的托里（Tori）。 在这项工作中，我们进一步走了一步。我们分析了可依赖的综合且近乎综合的哈密顿量的时间扰动。假设扰动会随着时间的流逝而衰减，我们证明了将来和过去的轨道存在与某些准二聚体溶液的存在。
In a previous work [Asymptotically quasiperiodic solutions for time-dependent Hamiltonians, arXiv preprint arXiv:2211.06623 (2022)], we consider time-dependent perturbations of a Hamiltonian vector field having an invariant torus supporting quasiperiodic solutions. Assuming the perturbation decays polynomially fast as time tends to infinity, we prove the existence of an asymptotic KAM torus. An asymptotic KAM torus is a time-dependent family of embedded tori converging as time tends to infinity to the invariant torus associated with the unperturbed system. Now, it is quite natural to wonder when we have the existence of a biasymptotic KAM torus. That is a continuous time-dependent family of embedded tori converging in the future and the past to suitable quasiperiodic invariant tori. In this work, we go one step further. We analyze time-dependent perturbations of integrable and near-integrable Hamiltonians. Assuming the perturbation decays polynomially fast in time, we prove the existence of orbit converging to some quasiperiodic solutions in the future and the past.
