| 书目名称 | KAM Theory and Semiclassical Approximations to Eigenfunctions | | 编辑 | Vladimir F. Lazutkin | | 视频video | http://file.papertrans.cn/542/541625/541625.mp4 | | 丛书名称 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati | | 图书封面 |  | | 描述 | It is a surprising fact that so far almost no books have been published on KAM theory. The first part of this book seems to be the first monographic exposition of this subject, despite the fact that the discussion of KAM theory started as early as 1954 (Kolmogorov) and was developed later in 1962 by Arnold and Moser. Today, this mathematical field is very popular and well known among physicists and mathematicians. In the first part of this .Ergebnisse.-Bericht, Lazutkin succeeds in giving a complete and self-contained exposition of the subject, including a part on Hamiltonian dynamics. The main results concern the existence and persistence of KAM theory, their smooth dependence on the frequency, and the estimate of the measure of the set filled by KAM theory. The second part is devoted to the construction of the semiclassical asymptotics to the eigenfunctions of the generalized Schrödinger operator. The main result is the asymptotic formulae for eigenfunctions and eigenvalues, using Maslov`s operator, for the set of eigenvalues of positive density in the set of all eigenvalues. An addendum by Prof. A.I. Shnirelman treats eigenfunctions corresponding to the "chaotic component" of th | | 出版日期 | Book 1993 | | 关键词 | Eigenvalue; Hamilton-Systeme; Hamiltonian systems; KAM Theorie; KAM theory; convergence; deduction; derivat | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-76247-5 | | isbn_softcover | 978-3-642-76249-9 | | isbn_ebook | 978-3-642-76247-5Series ISSN 0071-1136 Series E-ISSN 2197-5655 | | issn_series | 0071-1136 | | copyright | Springer-Verlag Berlin Heidelberg 1993 |
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