On first integrals of geodesic flows on a two-torus

DOI10.1134/S0081543816080150zbMath1362.37113arXiv1610.04822WikidataQ125824624 ScholiaQ125824624MaRDI QIDQ521555

Iskander A. Taimanov

Publication date: 11 April 2017

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04822

zbMATH Keywords

geodesicsoliton equationsdispersionless limitsquadratic first integral

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 (14)

Some remarks on high degree polynomial integrals of the magnetic geodesic flow on the two-dimensional torus ⋮ On the integrability of circulatory systems ⋮ Integrable magnetic geodesic flows on 2-surfaces ^* ⋮ Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for 2D standing coastal waves ⋮ Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom ⋮ Gyroscopic Chaplygin systems and integrable magnetic flows on spheres ⋮ 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 ⋮ Nonlinear long standing waves with support bounded by caustics or localized in the vicinity of a two-link trajectory ⋮ New examples of non-polynomial integrals of two-dimensional geodesic flows ^* ⋮ Integrable geodesic flows and metrisable second-order ordinary differential equations ⋮ On first integrals of two-dimensional geodesic flows ⋮ The dispersionless Veselov-Novikov equation: symmetries, exact solutions, and conservation laws ⋮ Asymptotic eigenfunctions of the operator \(\nabla D(x)\nabla\) defined in a two-dimensional domain and degenerating on its boundary and billiards with semi-rigid walls

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