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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 018 910 060
Author(s):
Perelomov, A. M.:
Shorttitle:
Classical integrable systems: Selected topics.
Source:
In: Olshanetsky, M. et al., Multiple facets of quantization and supersymmetry. Singsapore: World Scientific, 267-309 (2002). Michael Marinov memorial volume.
Classification:
81R12Relations with integrable systems
Primary Classification:
70H06Completely integrable systems and methods of integration
Secondary Classification:
70H08Nearly integrable Hamiltonian systems, KAM theory
Keywords:
Hamiltonian systems; Poisson structure; classical integrable systems; Lie algebras of symmetries; Calogero-Sutherland models; non-periodic Toda lattice; Euler top; Lotka-Volterra system; Halphen system; Lorentz model; Kermack-McKendrick models for epidemics
Review:


Many of the Perelomov's original papers are mostly appreciated
for their timeliness and high scientific standards rather than
accessibility. Somebody has to have told him: This time he
decided to write a review-type commentary on the relevance of the
Poisson structures for Hamiltonian systems and on the explicit
integration of the classical equations of motion of the
Calogero-Sutherland and Toda type in the more expanded form, more
immediately accessible to non-specialists, using many examples
and explicit illustrations. With the main attention constrained
to the A-series (of cases characterized by the special unitary
Lie algebra symmetry), the review might very well serve as an
expository introduction to the reading of the original papers in
their completeness and, in particular, to the detailed study of
his famous book ``A. M. Perelomov, Integrable systems of
classical mechanics and Lie algebras. I, Birkhaeuser, Basel,
1990".
Remarks to the editors:

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