We provide an extension of the Poincaré–Birkhoff Theorem for systems coupling linear components with twisting components. Applications are given both to weakly coupled Hamiltonian systems where, e.g., a superlinear or sublinear behaviour is assumed in the nonlinear part of the coupling in order to recover the needed twist conditions, and to local perturbations of superintegrable systems, showing the survival of a number of periodic solutions from a lower-dimensional torus.

中文翻译：

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耦合线性和扭曲：Poincaré–Birkhoff定理在哈密顿系统中的扩展

我们提供了庞加莱-伯克霍夫定理的扩展，适用于耦合线性分量与扭曲分量的系统。既适用于弱耦合的哈密顿系统，其中在耦合的非线性部分假设超线性或亚线性行为以恢复所需的扭转条件，也可应用于超可积系统的局部摄动，从而显示了许多生存低维圆环的周期解。