Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems

doi:10.1007/s11425-018-9311-7

CSpace > 数学所

	Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems
	Ding, Zhaodong 1; Shang, Zaijiu2,3
	2018-09-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	61 期号:9 页码:1567-1588
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.
关键词	Hamiltonian systems symplectic integrators KAM theory invariant tori twist symplectic mappings Russmann's non-degeneracy
DOI	10.1007/s11425-018-9311-7
语种	英语
资助项目	National Natural Science Foundation of China[11671392]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000442229900003
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31072
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.