This paper considers small perturbations of an integrable reversible system which has a degenerated lower dimensional invariant torus in some sense. In the presence of some higher-order terms, by some KAM technique and the stability of critical points of real analytic functions developed for hamiltonian systems, we prove the persistence of the degenerate lower dimensional invariant torus with prescribed frequencies without extra conditions on the perturbations besides the smallness. This result is an extension of the partial result of hamiltonian systems in Xu and You (Regul Chaotic Dyn 25(6):616–650, 2020) to reversible systems.

中文翻译：

---

可逆系统中具有规定频率的简并低维不变圆托的持久性

本文考虑了在某种意义上具有退化的低维不变环面的可积可逆系统的小扰动。在存在一些高阶项的情况下，通过某些KAM技术以及为汉弥尔顿系统开发的实际解析函数的临界点的稳定性，我们证明了退化的低维不变环具有规定频率的持久性，并且除了扰动外没有额外条件小。该结果是Xu和You中的哈密顿系统的部分结果（Regul Chaotic Dyn 25（6）：616–650，2020）的扩展。