Все это к делу отношения не имеет. Лично я против Фоменко ничего не имею. Как математик,
он вполне на уровне, не смотря на свой солидный возраст.
http://www.math.upatras.gr/~aegion/book.pdf
Anatoly T.Fomenko
Moscow State University, Russia
e-mail:
fomenko@mech.math.msu.su
Topology and Geometry of Integrable Hamiltonian
Systems on Lie algebras New Development.Abstract. New results in the theory of topological classi-
cation of integrable Hamiltonian systems where obtained in
the last years. Each system of dierential equations, which
is integrable in Liouville sense on symplectic manifold M,
generates the so called Liouville foliation, i.e. the foliation
of M into the union of tori and some singular bers which
are obtained as some gluings and degenerations of several
Liouville tori. The analysis of topology of Liouville foliaA
egion Conference on Topology 69
tions gives a lot of information about the behaviour of the
solutions of initial system of dierential equations. Such
systems appear in many concrete problems of mathematical
physics, algebra and topology.
Some time ago Mischenko and Fomenko proved fundamental
theorem, that each semisimple Lie algebra there
exists at least one integrable Hamiltonian system with polinomail
integrals on any orbit of general position in Lie algebra.
Then they formulated the conjecture that this is
true for any nite-dimensional Lie algebra. Many mathematicians
in the series of works proved this conjecture
for dierent types of Lie algebras. Recently the general
Mischenko-Fomenko conjecture was nally proved for any
Lie algebra by S.T.Sadetov. He discovered some new important
mechanism of polinomial integrability. Basing on
this result, Fomenko and his pupils obtained new theorems
clarifying the geometry of Lie algebras. In particular, for
all Lie algebras of low dimensions (up to 6) are discovered
the direct and explicit formulas for the polinomial integrals.