Titlebook: KAM Theory and Semiclassical Approximations to Eigenfunctions; Vladimir F. Lazutkin Book 1993 Springer-Verlag Berlin Heidelberg 1993 Eigen

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Beyond The Torie frequency playing the role of the parameter and ranging over a Cantor set ℰ. There are an infinite number of holes and gaps which are to be removed from the phase space to obtain the set occupied by KAM tori.

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Quasimodes Attached to a KAM Seter of quasimodes appears to equal the phase-space volume occupied by the KAM set divided by (2π.)., the elementary quantum-cell volume. The construction presented below is the most general one and involves no essential hypotheses.

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Proof of the Main Theoremin routines checking the inequalities necessary for the iterative process to occur correctly and their simple consequences. In §27 we summarize the results and establish that the objects obtained satisfy the conditions of the conclusion of Theorem 11.6.

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0071-1136 ographic 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 t