Topological classification of integrable geodesic flows in a potential field on the torus of revolution


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Abstract

A Liouville classification of integrable Hamiltonian systems which are the geodesic flows on 2-dimensional torus of revolution in a invariant potential field in the case of linear integral is obtained. This classification is obtained using the Fomenko–Zieschang invariant (marked molecules) of investigated systems. All types of bifurcation curves are described. Also a classification of singularities of the system solutions is obtained.

About the authors

D. S. Timonina

Faculty of Mechanics and Mathematics

Author for correspondence.
Email: darik93@yandex.ru
Russian Federation, Moscow, 119991

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