具有衰减非自治扰动的近可积哈密顿量的normal form理论中小divisor效应的可忽略性
Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations
摘要：
本文讨论了具有随时间缓慢衰减的非周期性含时扰动的近可积实解析哈密顿量的规范形的存在性问题。特别地，在等熵可积部分的情况下，系统可以被转换成精确的正规形，而不管频率向量的性质如何。一般情况下，治疗的有穷级规范化技术通常用于Nekhoroshev参数的适当适应。关键是，在这种情况下，所谓的“几何部分”是不必要的。因此，除了解析性之外，不需要关于可积部分的假设。这项工作基于A.Giorgilli等人开发的两种不同的微扰方法，是一个概括的技术所使用的相同的作者来处理更具体的非周期性的时间依赖性问题。
英文摘要：
The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous integrable part, the system can be cast in an exact normal form, regardless of the properties of the frequency vector. The general case is treated by a suitable adaptation of the finite order normalization techniques usually used for Nekhoroshev arguments. The key point is that the so called "geometric part" is not necessary in this case. As a consequence, no hypotheses on the integrable part are required, apart from analyticity. The work, based on two different perturbative approaches developed by A.Giorgilli et al., is a generalisation of the techniques used by the same authors to treat more specific aperiodically time-dependent problems.
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