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Mat. Sb., 2018, Volume 209, Number 5, Pages 145–165 (Mi msb8946)  

Graph-manifolds and integrable Hamiltonian systems

K. I. Solodskikh

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

Keywords: Reidemeister torsion, Waldhausen graph-manifold, Fomenko-Zieschang invariants, marked molecules, Hamiltonian systems.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-6399.2018.1
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).


DOI: https://doi.org/10.4213/sm8946

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English version:
Sbornik: Mathematics, 2018, 209:5, 739–758

Bibliographic databases:

UDC: 514.853
MSC: Primary 37J35; Secondary 37C15
Received: 23.03.2017 and 19.02.2018

Citation: K. I. Solodskikh, “Graph-manifolds and integrable Hamiltonian systems”, Mat. Sb., 209:5 (2018), 145–165; Sb. Math., 209:5 (2018), 739–758

Citation in format AMSBIB
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