Non-integrability of the truncated Toda lattice Hamiltonian at any order

DOI10.1007/BF01224900zbMath0671.35074MaRDI QIDQ1119836

Haruo Yoshida

Publication date: 1988

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemspolynomial potentialanalytic integralnon-integrabletruncated three-particle Toda lattice

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) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Cites Work

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• A criterion for non-integrability of Hamiltonian systems with nonhomogeneous potentials
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Non-integrability of Hénon-Heiles system and a theorem of Ziglin
• Existence of exponentially unstable periodic solutions and the non- integrability of homogeneous Hamiltonian systems
• Non-integrability of the fourth-order truncated Toda Hamiltonian
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• On the non-integrability of some generalized Toda lattices
• Theory of nonlinear lattices
• Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization
• Approximations of the 3-particle Toda lattice
• Integrals of the Toda lattice
• The Toda lattice. II. Existence of integrals

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