POLYNOMIAL INTEGRALS OF GEODESIC FLOWS ON A TWO-DIMENSIONAL TORUS

DOI10.1070/SM1995v083n02ABEH003601zbMath0841.53039OpenAlexW2057983653WikidataQ114394627 ScholiaQ114394627MaRDI QIDQ4863198

N. V. Denisova, Valery V. Kozlov

Publication date: 16 June 1996

Published in: Russian Academy of Sciences. Sbornik Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm1995v083n02abeh003601

zbMATH Keywords

Riemannian manifoldHamiltonian systemsgeodesic flow

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Geodesics in global differential geometry (53C22) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (14)

On the integrability of circulatory systems ⋮ Killing tensors on tori ⋮ On two-dimensional Hamiltonian systems with sixth-order integrals of motion ⋮ Symmetries of a flat cosymbol algebra of differential operators ⋮ On some properties of semi-Hamiltonian systems arising in the problem of integrable geodesic flows on the two-dimensional torus ⋮ Rational integrals of a natural mechanical system on the 2-torus ⋮ Rational integrability of trigonometric polynomial potentials on the flat torus ⋮ On first integrals of two-dimensional geodesic flows ⋮ On momentum-polynomial integrals of a reversible Hamiltonian system of a certain form ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ New Families of Integrable Two-Dimensional Systems with Quartic Second Integrals ⋮ On first integrals of geodesic flows on a two-torus ⋮ Integrable magnetic geodesic flows on 2-torus: new examples via quasi-linear system of PDEs ⋮ Integrals polynomial in velocity for two-degrees-of-freedom dynamical systems whose configuration space is a torus

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