KAM Theory and Semiclassical Approximations to Eigenfunctions

KAM Theory and Semiclassical Approximations to Eigenfunctions by Vladimir F. Lazutkin.

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...

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Bibliographic Details
Main Author: Lazutkin, Vladimir F. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993.
Edition:1st ed. 1993.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 24
Springer eBook Collection.
Subjects:
Mathematical analysis.
Analysis (Mathematics).
Quantum computers.
Spintronics.
Quantum physics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • List of General Mathematical Notations
  • I. KAM Theory
  • I. Symplectic Dynamical Systems
  • II. KAM Theorems
  • III. Beyond the Tori
  • IV. Proof of the Main Theorem
  • II. Eigenfunctions Asymptotics
  • V. Laplace-Beltrami-Schrödinger Operator and Quasimodes
  • VI. Maslov’s Canonical Operator
  • VII. Quasimodes Attached to a KAM Set
  • Addendum (by A.I. Shnirelman). On the Asymptotic Properties of Eigenfunctions in the Regions of Chaotic Motion
  • Appendix I. Manifolds
  • Appendix II. Derivatives of Superposition
  • Appendix III. The Stationary Phase Method
  • References.

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