First integrals from conformal symmetries: Darboux-Koenigs metrics and beyond

DOI10.1016/j.geomphys.2019.07.006zbMath1430.37063arXiv1804.06904OpenAlexW2797565660MaRDI QIDQ2331496

Allan P. Fordy

Publication date: 29 October 2019

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.06904

zbMATH Keywords

Hamiltonian systemPoisson algebraquantum integrabilityconformal algebrasuper-integrabilityDarboux-Koenigs metrics

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geometry and quantization, symplectic methods (81S10) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Hamilton-Jacobi equations in mechanics (70H20) Poisson algebras (17B63) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Related Items (6)

Integrable and superintegrable extensions of the rational Calogero–Moser model in three dimensions ⋮ Superintegrable systems on 3 dimensional conformally flat spaces ⋮ Two-dimensional integrable systems with position-dependent mass via complex holomorphic functions ⋮ Koenigs theorem and superintegrable Liouville metrics ⋮ Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces ⋮ The role of commuting operators in quantum superintegrable systems

Cites Work

• Two-dimensional superintegrable metrics with one linear and one cubic integral
• Poisson algebras and 3D superintegrable Hamiltonian systems
• Quantum super-integrable systems as exactly solvable models
• Classical and quantum superintegrability with applications
• Quantum integrability of quadratic Killing tensors
• Superintegrability in a two-dimensional space of nonconstant curvature
• Superintegrable systems in Darboux spaces
• Unnamed Item
• Unnamed Item

This page was built for publication: First integrals from conformal symmetries: Darboux-Koenigs metrics and beyond