1. 毕业设计（论文）的内容和要求

作为哈密顿系统的离散形式，辛映射继承了哈密顿系统的一些性质，比如具有类似的结构。

但是辛映射没有固定的规范型，因而在处理小分母问题时，会有很多困难。

本论文研究辛映射的小分母问题。

2. 参考文献

【1】S. Jiang*. Gevrey-smoothness of invariant tori for nearly integrable simplectic mappings. [J] Electronic Journal of Differential Equations. Vol. 2017 (2017), No. 159, pp. 1#8211;17,2017. (SCI) 【2】. S. Jiang*. A KAM theorem for lower dimensional elliptic invariant tori of nearly integrable symplectic mappings. [J Journal of Function Spaces#8232;.Volume (2017), Article ID 3719395, 10 pages,2017. (SCI) 【3】 S. Jiang*. Gevrey-smoothness of lower dimensionalhyperbolic invariant tori for nearly integrable symplectic mappings . [J]Journal of Inequalities and Applications (2017) 2017:39 (SCI) 【4】 V. Arnold; Proof of A.N. Kolmogorov#8217;s theorem on conservation of conditionally periodic mo- tions under small perturbations of the hamiltonian function, Uspeki Matematicheskii Nauk, (18) 1963, 13#8211;40. 【5】 A. D. Bruno; Analytic form of differential equations, Trudy Moskovskogo Matematicheskogo Obshchestva, 26 (1972), 199-239. 【6】 Q.-Y. Bi, J.-X. Xun; Persistence of Lower Dimensional Hyperbolic Invariant Tori for Nearly Integrable Symplectic Mappings, Qualitative Theory of Dynamical Systems, 13 (2014), 269- 288. Q.-Y. Bi, J.-X. Xun; Persistence of Lower Dimensional Hyperbolic Invariant Tori for Nearly Integrable Symplectic Mappings, Qualitative Theory of Dynamical Systems, 13 (2014), 269- 288.

3. 毕业设计（论文）进程安排

第1-2周 听老师讲课，理解类牛顿迭代（kam）思路。

第3-5周 阅读文献，深入理解kam思路。

第6-12周 论文初稿撰写，定期向老师汇报。