Abstract:
We study the topology of the three-dimensional constant-energy manifolds of
integrable Hamiltonian systems realizable in the form of a special class of
so-called ‘molecules’. Namely, for this class of manifolds the Reidemeister
torsion is calculated in terms of the Fomenko-Zieschang invariants.
A connection between the torsion of a constant-energy manifold and stable
periodic trajectories is found.
Bibliography: 17 titles.
This research was conducted within the framework of the Programme of the President of the Russian Federation for state support of leading scientific schools of the Russian Federation (grant no. НШ-6399.2018.1).
\Bibitem{Sol18}
\by K.~I.~Solodskikh
\paper Graph-manifolds and integrable Hamiltonian systems
\jour Sb. Math.
\yr 2018
\vol 209
\issue 5
\pages 739--758
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Linking options:
https://www.mathnet.ru/eng/sm8946
https://doi.org/10.1070/SM8946
https://www.mathnet.ru/eng/sm/v209/i5/p145
This publication is cited in the following 3 articles:
A. T. Fomenko, V. A. Kibkalo, “Topology of Liouville foliations of integrable billiards on table-complexes”, European Journal of Mathematics, 8:4 (2022), 1392
A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrability in geometry and physics. New scope and new potential”, Moscow University Mathematics Bulletin, 74:3 (2019), 98–107
Anatoly T. Fomenko, Kirill I. Solodskih, Understanding Complex Systems, Modern Mathematics and Mechanics, 2019, 13
Citation in format AMSBIB
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