Polynomial constants of motion for Calogero-type systems in three dimensions

Abstract

We give an explicit and concise formula for higher-degree polynomial first integrals of a family of Calogero-type Hamiltonian systems in dimension three. These first integrals, together with the already known ones, prove the maximal superintegrability of the systems.

A small flaw in the proof of Theorem 3 has been amended. Some remarks about dihedral symmetries and superintegrability have been added

References in corpus (8)

• An infinite family of solvable and integrable quantum systems on a plane
• Periodic orbits for an infinite family of classical superintegrable systems
• Superintegrability and higher order constants for quantum systems
• Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces
• Superintegrable 3-body systems on the line
• Families of classical subgroup separable superintegrable systems
• Superintegrable three body systems in one dimension and generalizations
• Searching for integrable Hamiltonian systems with Platonic symmetries

Cited by in corpus (11)

• Higher-order superintegrability of separable potentials with a new approach to the Post-Winternitz system
• Superintegrable systems with spin and second-order integrals of motion
• Third-order superintegrable systems separable in parabolic coordinates
• Generalizations of a method for constructing first integrals of a class of natural Hamiltonians and some remarks about quantization
• A new approach to the higher-order superintegrability of the Tremblay-Turbiner-Winternitz system
• The Tremblay-Turbiner-Winternitz system as extended Hamiltonian
• Extensions of Hamiltonian systems dependent on a rational parameter
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Extended Hamiltonians and shift, ladder functions and operators
• Extensions of natural Hamiltonians
• Extensions of non-natural Hamiltonians