高维小扭转映射不变环面的存在性

Existence of Invariant Tori for Small Twist Mappings with Higher Dimensions

考虑角度变量和作用变量具有不同维数的高维近可积小扭转映射不变环面的存在性,通过构造KAM迭代的方法,证明高维近可积小扭转映射在满足Rüssmann非退化条件及相交性条件下存在一族不变环面.

We considered the existence of invariant tori for nearly integrable small twist mappings whose dimensional numbers of angles and actions variables were different.By constructing KAM iteration method,we proved that the nearly integrable small twist mappings with high dimension possessed a family of invariant tori under the Rüssmann non-degeneracy condition and the intersection condition.