On rational integrals of geodesic flows

DOI10.1134/S156035471406001XzbMath1343.37047MaRDI QIDQ892750

Valery V. Kozlov

Publication date: 12 November 2015

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

Cauchy-Kovalevskaya theoremconformal coordinatesirreducible integralsrational integral

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamics induced by flows and semiflows (37C10) Cauchy-Kovalevskaya theorems (35A10) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (13)

On the extendability of Noether's integrals for orbifolds of constant negative curvature ⋮ Integrable magnetic geodesic flows on 2-surfaces ^* ⋮ Lax pairs and special polynomials associated with self-similar reductions of Sawada -- Kotera and Kupershmidt equations ⋮ On a class of quadratic conservation laws for Newton equations in Euclidean space ⋮ Rational integrals of a natural mechanical system on the 2-torus ⋮ New examples of non-polynomial integrals of two-dimensional geodesic flows ^* ⋮ On the rational integrals of two-dimensional natural systems ⋮ On the geometric and analytical properties of the anharmonic oscillator ⋮ Integrable geodesic flows and metrisable second-order ordinary differential equations ⋮ On first integrals of two-dimensional geodesic flows ⋮ Projective dynamics and first integrals ⋮ Rational integrals of 2-dimensional geodesic flows: new examples ⋮ Rational integrals of the second degree of two-dimensional geodesic equations

Cites Work

• Projective dynamics and first integrals
• A note on the integrability conditions for the existence of rational first integrals of the geodesic equations in a Riemannian space
• A class of empty spacetimes admitting a rational first integral of the geodesic equation
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