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Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems
Ding, Zhaodong1; Shang, Zaijiu2,3
2018-09-01
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume61Issue:9Pages:1567-1588
AbstractIn 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.
KeywordHamiltonian systems symplectic integrators KAM theory invariant tori twist symplectic mappings Russmann's non-degeneracy
DOI10.1007/s11425-018-9311-7
Language英语
Funding ProjectNational Natural Science Foundation of China[11671392]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000442229900003
PublisherSCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31072
Collection数学所
Affiliation1.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
Recommended Citation
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.
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