Symmetry reduction and superintegrable Hamiltonian systems

Abstract

We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems are maximally superintegrable. We also discuss the reduction method used in this article and its possible generalization to other maximally superintegrable systems.

9 pages

References in corpus (4)

• Reduction of superintegrable systems: the anisotropic harmonic oscillator
• Superintegrability of the Caged Anisotropic Oscillator
• A New Superintegrable Hamiltonian
• Reduction Procedures in Classical and Quantum Mechanics

Cited by in corpus (15)

• Classical and Quantum Superintegrability with Applications
• An infinite family of superintegrable deformations of the Coulomb potential
• Classical ladder operators, polynomial Poisson algebras and classification of superintegrable systems
• Construction of classical superintegrable systems with higher order integrals of motion from ladder operators
• Higher-order superintegrability of separable potentials with a new approach to the Post-Winternitz system
• Families of classical subgroup separable superintegrable systems
• A new approach to the higher-order superintegrability of the Tremblay-Turbiner-Winternitz system
• A new proof of the higher-order superintegrability of a noncentral oscillator with inversely quadratic nonlinearities
• Quantum Integrals from Coalgebra Structure
• Generalized Lenard Chains, Separation of Variables and Superintegrability
• Are all classical superintegrable systems in two-dimensional space linearizable?
• The ${\mathfrak{sl}}_2(\mathbb{R})$ coalgebra symmetry and the superintegrable discrete-time systems
• On higher-dimensional superintegrable systems: A new family of classical and quantum Hamiltonian models
• Group-theoretical approach to a non-central extension of the Kepler-Coulomb problem
• Lie-algebraic interpretation of the maximal superintegrability and exact solvability of the Coulomb-Rosochatius potential in n dimensions