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Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems

文献类型：期刊论文

作者Ding, Zhaodong1; Shang, Zaijiu2,3
刊名SCIENCE CHINA-MATHEMATICS
出版日期2018-09-01
卷号61期号:9页码:1567-1588
关键词Hamiltonian systems symplectic integrators KAM theory invariant tori twist symplectic mappings Russmann's non-degeneracy
ISSN号1674-7283
DOI10.1007/s11425-018-9311-7
英文摘要In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Russmann'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.
资助项目National Natural Science Foundation of China[11671392]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000442229900003
出版者SCIENCE PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/31071]  
专题数学所
通讯作者Ding, Zhaodong
作者单位1.Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, HUA Loo Keng Key Lab Math, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Ding, Zhaodong,Shang, Zaijiu. Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems[J]. SCIENCE CHINA-MATHEMATICS,2018,61(9):1567-1588.
APA Ding, Zhaodong,&Shang, Zaijiu.(2018).Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems.SCIENCE CHINA-MATHEMATICS,61(9),1567-1588.
MLA Ding, Zhaodong,et al."Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems".SCIENCE CHINA-MATHEMATICS 61.9(2018):1567-1588.

入库方式： OAI收割

来源：数学与系统科学研究院

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