Minimal invariant tori in the resonant regions for nearly integrable Hamiltonian systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Minimal invariant tori in the resonant regions for nearly integrable Hamiltonian systems

Authors:	Chong-Qing Cheng

Institution:	Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China -- and -- The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong, China

Abstract:	Consider a real analytical Hamiltonian system of KAM type that has degrees of freedom () and is positive definite in . Let $\Omega =\{\omega\in \mathbb R^n \vert\langle \bar k,\omega\rangle =0, \bar k\in\mathbb Z^n\}$ . In this paper we show that for most rotation vectors in $\Omega$ , in the sense of ()-dimensional Lebesgue measure, there is at least one ()-dimensional invariant torus. These tori are the support of corresponding minimal measures. The Lebesgue measure estimate on this set is uniformly valid for any perturbation.

Keywords:	KAM method invariant torus minimal measure

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