通过可逆性可积性

摘要：

引入了一类带函数参数的左不变二阶可逆系统，该系统表现出鲁棒可积性现象：相空间的一个开的稠密子集充满了携带拟周期运动的不变环面，并且在该类内扰动下，这种行为持续存在.实解析保体积系统是一类在开子集上具有正的李雅普诺夫指数，且补集上充满不变环面的系统。

英文摘要：

A class of left-invariant second order reversible systems with functional parameter is introduced which exhibits the phenomenon of robust integrability: an open and dense subset of the phase space is filled with invariant tori carrying quasi-periodic motions, and this behavior persists under perturbations within the class. Real-analytic volume preserving systems are found in this class which have positive Lyapunov exponents on an open subset, and the complement filled with invariant tori.

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