This paper focuses on the persistence of lower-dimensional tori in reversible systems with hyperbolic-type degenerate equilibrium point under small perturbations. Moreover, the dimension of degenerate variable is greater than or equal to 2. By KAM iteration and the Topological degree theorem, we prove that the invariant torus with given frequency persists under small perturbations.

中文翻译：

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小扰动下双曲型退化平衡点可逆系统中低维环面的持久性

本文重点研究了小扰动下双曲型退化平衡点可逆系统中低维环面的持久性。此外，退化变量的维数大于或等于2。通过KAM迭代和拓扑度定理，我们证明给定频率的不变环在小扰动下仍然存在。