Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree --3

DOI10.1016/j.physd.2011.09.003zbMath1237.34047OpenAlexW2043065437MaRDI QIDQ655552

Jaume Llibre, Adam Mahdi, Claudia Valls

Publication date: 4 January 2012

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/150419

zbMATH Keywords

Hamiltonian system with two degrees of freedomhomogeneous potential of degree \(-3\)polynomial integrability

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items

Polynomial integrability of Hamiltonian systems with homogeneous potentials of degree \(k\), Analytic integrability of Hamiltonian systems with exceptional potentials, On the polynomial integrability of the critical systems for optimal eigenvalue gaps, On the integrability of the Hamiltonian systems with homogeneous polynomial potentials, Integrability of the Hide-Skeldon-Acheson dynamo, Integrability conditions of geodesic flow on homogeneous Monge manifolds, Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree \(-4\)

Cites Work

• Unnamed Item
• Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree - 2
• Analytic-non-integrability of an integrable analytic Hamiltonian system
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Multiparticle systems. The algebra of integrals and integrable cases
• A theory of exact and approximate configurational invariants
• Analytic non-integrable Hamiltonian systems and irregular singularity
• Non-integrability of some Hamiltonians with rational potentials
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• All meromorphically integrable 2D Hamiltonian systems with homogeneous potential of degree 3
• Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces
• Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential
• TOPOLOGICAL OBSTRUCTIONS TO INTEGRABILITY OF GEODESIC FLOWS ON NON-SIMPLY-CONNECTED MANIFOLDS
• Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes
• Analytic integrability of Hamiltonian systems with a homogeneous polynomial potential of degree 4
• Differential Galois theory and non-integrability of Hamiltonian systems
• New examples of integrable geodesic flows.