Global behaviors of weak KAM solutions for exact symplectic twist maps

doi:10.1016/j.jde.2020.04.017

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	Global behaviors of weak KAM solutions for exact symplectic twist maps
	Zhang, Jianlu 1,2
	2020
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	269 期号:7 页码:5730-5753
摘要	We investigated several global behaviors of the weak KAM solutions u(c)(x, t) parametrized by c is an element of H-1(T, R). For the suspended Hamiltonian H(x, p, t) of the exact symplectic twist map, we could find a family of weak KAM solutions u(c)(x, t) parametrized by c(sigma) is an element of H-1(T, R) with c(sigma) continuous and monotonic and partial derivative(t)u(c) + H(x, partial derivative(x)u(c) + c, t) = alpha(c), a.e. (x, t) is an element of T-2, such that sequence of weak KAM solutions {u(c)}(c is an element of H1(T,R)) is 1/2-Holder continuity of parameter sigma is an element of R. Moreover, for each generalized characteristic (no matter regular or singular) solving {(x) over dot(s) is an element of co[partial derivative H-p(x(s), c + D(+)u(c)(x(s), s + t), s + t)], x(0) = x(0), (x(0), t) is an element of T-2, we evaluate it by a uniquely identified rotational number omega(c) is an element of H-1(T, R). This property leads to a certain topological obstruction in the phase space and causes local transitive phenomenon of trajectories. Besides, we discussed this applies to high-dimensional cases. (C) 2020 Elsevier Inc. All rights reserved.
关键词	Exact syplectic twist map Aubry Mather theory Hamilton Jacobi equation Generalized characteristics Weak KAM solution Transition chain
DOI	10.1016/j.jde.2020.04.017
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000549985200007
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51835
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Jianlu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Math Inst, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Jianlu. Global behaviors of weak KAM solutions for exact symplectic twist maps[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2020,269(7):5730-5753.
APA	Zhang, Jianlu.(2020).Global behaviors of weak KAM solutions for exact symplectic twist maps.JOURNAL OF DIFFERENTIAL EQUATIONS,269(7),5730-5753.
MLA	Zhang, Jianlu."Global behaviors of weak KAM solutions for exact symplectic twist maps".JOURNAL OF DIFFERENTIAL EQUATIONS 269.7(2020):5730-5753.