首页|The KAM theorem on the modulus of continuity about parameters

The KAM theorem on the modulus of continuity about parameters

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In this paper,we study the Hamiltonian systems H(y,x,ξ,ε)=(ω(ξ),y)+εP(y,x,ξ,ε),where ω and P are continuous about ξ.We prove that persistent invariant tori possess the same frequency as the unperturbed tori,under a certain transversality condition and a weak convexity condition for the frequency mapping ω.As a direct application,we prove a Kolmogorov-Arnold-Moser(KAM)theorem when the perturbation P holds arbitrary Hölder continuity with respect to the parameter ξ.The infinite-dimensional case is also considered.To our knowledge,this is the first approach to the systems with the only continuity in the parameter beyond Hölder's type.

Hamiltonian systemsinvariant torifrequency-preservingweak regularity

Zhicheng Tong、Jiayin Du、Yong Li

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School of Mathematics,Jilin University,Changchun 130012,China

Institute of Mathematics,Jilin University,Changchun 130012,China

School of Mathematics and Statistics,Center for Mathematics and Interdisciplinary Sciences,Northeast Normal University,Changchun 130024,China

National Basic Research Program of China国家自然科学基金国家自然科学基金国家自然科学基金Project of Science and Technology Development of Jilin ProvinceProject of Science and Technology Development of Jilin Province吉林省自然科学基金

2013CB8341001207117511171132115710652017C028-120190201302JC20200201253JC

2024

10.1007/s11425-022-2102-5

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(3)
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