Integrability and orbits in quartic polynomial potentials

DOI10.1063/1.528546zbMath0896.58033OpenAlexW1982663260MaRDI QIDQ4712701

Paul W. Cleary

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.528546

zbMATH Keywords

integrabilitymovable singularitiesPainlevé analysisquartic polynomial potentials

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) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Cites Work

• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• Existence of exponentially unstable periodic solutions and the non- integrability of homogeneous Hamiltonian systems
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
• Explicit integrability for Hamiltonian systems and the Painlevé conjecture
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes
• The stability of periodic orbits in the three-body problem
• Necessary condition for the existence of algebraic first integrals

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