Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems  

作　　者：Zhaodong Ding Zaijiu Shang 

机构地区：[1]School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China [2]HUA Loo-Keng Key Laboratory of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China [3]School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Science China Mathematics》2018年第9期1567-1588,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11671392)

摘　　要：In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rssmann's non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an estimate of the measure of the set occupied by the invariant tori in the phase space. On an invariant torus,numerical solutions are quasi-periodic with a diophantine frequency vector of time step size dependence. These results generalize Shang's previous ones(1999, 2000), where the non-degeneracy condition is assumed in the sense of Kolmogorov.In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rssmann＇s non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an estimate of the measure of the set occupied by the invariant tori in the phase space. On an invariant torus,numerical solutions are quasi-periodic with a diophantine frequency vector of time step size dependence. These results generalize Shang＇s previous ones（1999, 2000）, where the non-degeneracy condition is assumed in the sense of Kolmogorov.

关 键 词：Hamiltonian systems symplectic integrators KAM theory invariant tori twist symplectic mappings Rüissmann＇s non-degeneracy 

分 类 号：O241.81[理学—计算数学]