We review a recent application of the ideas of normal form theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference from the standard case consists in the non-uniqueness of the normal form and the total absence of the small divisors problem. The exposition is quite general, so as to allow extensions to the case of more non-periodic coordinates, and more functional settings. Here, for simplicity, we work in the real-analytic class.

中文翻译：

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非准周期范式理论

我们回顾了范式理论思想最近在系统（哈密顿系统或一般 ODE）中的应用，其中扰动项在一个坐标变量中不是周期性的。与标准情况的主要区别在于范式的非唯一性和完全不存在小除数问题。阐述相当笼统，以便可以扩展到更多非周期坐标的情况，以及更多的功能设置。在这里，为了简单起见，我们在实分析类中工作。