Rational integrals of a natural mechanical system on the 2-torus

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Dynamical systems in classical and celestial mechanics (37N05) Ordinary differential equations and systems on manifolds (34C40)

Related Items (5)

Integrable magnetic geodesic flows on 2-surfaces ^* ⋮ On the rational integrals of two-dimensional natural systems ⋮ On the geometric and analytical properties of the anharmonic oscillator ⋮ On first integrals of two-dimensional geodesic flows ⋮ Rational integrals of 2-dimensional geodesic flows: new examples

Cites Work

Unnamed Item
Fourth-degree polynomial integrals of a natural mechanical system on a two-dimensional torus
Integrable geodesic flows on 2-torus: formal solutions and variational principle
Meromorphic solutions of generalized inviscid Burgers' equations and a family of quadratic PDEs
Rational integrals of the second degree of two-dimensional geodesic equations
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
Rich quasi-linear system for integrable geodesic flows on 2-torus
On rational integrals of geodesic flows
A note on the integrability conditions for the existence of rational first integrals of the geodesic equations in a Riemannian space
First integrals that are polynomial in momenta for a mechanical system on a two-dimensional torus
A class of empty spacetimes admitting a rational first integral of the geodesic equation
Rational integrability of trigonometric polynomial potentials on the flat torus
New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces
Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels
Classical mechanical systems with one-and-a-half degrees of freedom and Vlasov kinetic equation
Cubic and quartic integrals for geodesic flow on 2-torus via a system of the hydrodynamic type
Remarks on polynomial integrals of higher degrees for reversible systems with toral configuration space
On polynomial integrals of a mechanical system on a two-dimensional torus
ON THE INTEGRABILITY OF HAMILTONIAN SYSTEMS WITH TORAL POSITION SPACE
Polynomial integrals for a Hamiltonian system and breakdown of smooth solutions for quasi-linear equations
Polynomial integrals of reversible mechanical systems with a two-dimensional torus as the configuration space
THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
POLYNOMIAL INTEGRALS OF GEODESIC FLOWS ON A TWO-DIMENSIONAL TORUS
The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body

This page was built for publication: Rational integrals of a natural mechanical system on the 2-torus