This paper demonstrates sufficient conditions for the existence of a positive measure set of invariant KAM tori in a singly thermostated, 1 degree-of-freedom hamiltonian vector field. This result is applied to 4 important single thermostats in the literature and it is shown that in each case, if the hamiltonian is real-analytic and well-behaved, then the thermostated system always has a positive measure set of invariant KAM tori for sufficiently weak coupling and high temperature. This extends results of Legoll, Luskin & Moeckel.

中文翻译：

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一类单恒温哈密顿量的不变环

本文证明了在单恒温、1 自由度哈密顿矢量场中存在不变 KAM 环的正测度集的充分条件。这个结果被应用于文献中的 4 个重要的单个恒温器，并且表明在每种情况下，如果哈密顿量是实解析的并且表现良好，那么恒温系统对于足够弱的 KAM tori 总是有一个正测度集耦合和高温。这扩展了 Legoll、Luskin 和 Moeckel 的结果。