Kam Theory and Semiclassical Approximations to Eigenfunctions: Vol 24 (Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics) - Hardcover

Lazutkin, Vladimir F.

Hardcover

ISBN 10: 3540533893 ISBN 13: 9783540533894

Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1993

Inhaltsangabe

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 Schrodinger 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 the phase space.

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Reseña del editor

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 the phase space.

Reseña del editor

This monograph contains a series of research papers on KAM theory. In the first, 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 semi-classical asymptotics to the eigenfunctions of the generalized Schroedinger operator. The main result is the asymptotic formulae for eigenfunctions and eigen values, using Maslov's operator, for the set of eigen values of positive density in the set of all eigenvalues. An addendum by A.I. Shnirelman treats eigenfunctions corresponding to the "chaotic component" of the phase space.

Details zur Ausgabe

• Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Erscheinungsdatum: 1993
• Sprache: Englisch
• ISBN 10: 3540533893
• ISBN 13: 9783540533894
• Einband: Tapa dura
• Anzahl der Seiten: 396
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland