Application of classification theory for integrable Hamiltonian systems to geodesic flows on 2-sphere and 2-torus and to the description of the topological structure of momentum mapping near singular points

DOI10.1007/BF02363855zbMath0855.58046OpenAlexW1995270306MaRDI QIDQ1917799

A. T. Fomenko, Alexei V. Bolsinov

Publication date: 16 February 1997

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02363855

zbMATH Keywords

surveyclassificationcomplexity2-spheretopological invariantsRiemannian metricsintegrable geodesic flows2-torusnumerical invariant

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (1)

The Bertrand's manifolds with equators

Cites Work

• Supramenability and the problem of occurrence of free semigroups
• ON THE INTEGRABILITY OF HAMILTONIAN SYSTEMS WITH TORAL POSITION SPACE
• Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity
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