Nonintegrability of the Armbruster--Guckenheimer--Kim Quartic Hamiltonian Through Morales--Ramis Theory

DOI10.1137/16M1080689zbMath1384.37069arXiv1710.00227OpenAlexW2945028955MaRDI QIDQ4608079

Teresinha J. Stuchi, Martha Alvarez-Ramírez, Primitivo Belén Acosta-Humánez

Publication date: 15 March 2018

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.00227

zbMATH Keywords

Schrödinger equationdifferential Galois theoryHamiltonian integrabilityLegendre equation

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Differential algebra (12H05) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

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Cites Work

• On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
• Galoisian approach to integrability of Schrödinger equation
• Galoisian obstructions to integrability of Hamiltonian systems. II.
• Non-integrability of some Hamiltonians with rational potentials
• Non-integrability of the truncated Toda lattice Hamiltonian at any order
• Galoisian obstructions to integrability of Hamiltonian systems. I.
• Periodic orbits and non-integrability of Armbruster-Guckenheimer-Kim potential
• Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential
• Computing necessary integrability conditions for planar parametrized homogeneous potentials
• Differential Galois theory and non-integrability of Hamiltonian systems
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