Rational integrability of trigonometric polynomial potentials on the flat torus

DOI10.1134/S1560354717040049zbMath1385.37073arXiv1702.01432MaRDI QIDQ1701460

Thierry Combot

Publication date: 23 February 2018

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

Full work available at URL: https://arxiv.org/abs/1702.01432

zbMATH Keywords

integrabilityToda latticedifferential Galois theorytrigonometric polynomial

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items (4)

Integrable magnetic geodesic flows on 2-surfaces ^* ⋮ Rational integrals of a natural mechanical system on the 2-torus ⋮ 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
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• On an integrable case of Kozlov-Treshchev Birkhoff integrable potentials
• The finite Toda lattices
• Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization
• Rational parametrization of surfaces
• Lifting and recombination techniques for absolute factorization
• Necessary and sufficient conditions for the polynomial integrability of generalized Toda chains
• 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
• POLYNOMIAL INTEGRALS OF HAMILTONIAN SYSTEMS WITH EXPONENTIAL INTERACTION
• ON THE INTEGRABILITY OF HAMILTONIAN SYSTEMS WITH TORAL POSITION SPACE
• The toda flow on a generic orbit is integrable
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• Polynomial integrals of reversible mechanical systems with a two-dimensional torus as the configuration space
• POLYNOMIAL INTEGRALS OF GEODESIC FLOWS ON A TWO-DIMENSIONAL TORUS
• Lax formalism for a family of integrable Toda-related n-particle systems

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