AI 中文总结
该研究针对与刚性旋转实解析共轭的扭转映射，在Gevrey-γ扰动下，采用参数化直接KAM方法，证明了满足更强条件时其不变图仍可持久存在，拓展了经典KAM理论的适用范围。
AI 中文摘要
我们研究扭转映射不变图的持久性，这类映射具有最强动力学，即与刚性旋转实解析共轭，在Gevrey-γ（γ∈[0,1]）扰动下的情况。通过提升扰动本身的正则性，我们证明，当扰动大小和频率约束超出经典KAM理论及法双曲不变流形理论的要求时，具有最强动力学的不变图仍能保持存在。这些结果的证明基于参数化直接KAM方法。
英文摘要
We consider the persistence for invariant graphs of twist maps that exhibit the strongest possible dynamics, namely those real-analytically conjugate to rigid rotations, under Gevrey-$γ$ ($γ\in [0,1]$) perturbations. By enhancing the regularity of the perturbation itself, we show that invariant graphs with the strongest dynamics can persist even when the size of the perturbation and the constraints on the frequency go beyond the requirements of classical KAM theory and the theory of normally hyperbolic invariant manifolds. The proofs of these results are based on a parameterized direct KAM method.
CommentsThere is a gap in the proof of Theorem 2 in the paper, especially regarding the key lemma in the resonance renormalization procedure (Lemma A.4). In the general setting, this lemma does not apply to dissipative models
