On the maximal superintegrability of strongly isochronous Hamiltonians

Abstract

We study strongly isochronous Hamiltonians that generate periodic time evolution with the same basic period for a dense set of initial values. We explain that all such Hamiltonians are maximally superintegrable, and show that if the system is subjected to Hamiltonian reduction based on a compact symmetry group and certain conditions are met, then the reduced Hamiltonian is strongly isochronous with the original basic period. We utilize these simple observations for demonstrating the maximal superintegrability of rational spin Calogero--Moser type models in confining harmonic potential.

arXiv comment19 pages, v2: corrected 3 minor sign errors

References in corpus (6)

• Classical and Quantum Superintegrability with Applications
• Multicomponent Calogero Model of $B_N$-Type Confined in Harmonic Potential
• Integrable spin Calogero-Moser systems
• Superintegrability of Calogero-Moser systems associated with the cyclic quiver
• Integrable multi-Hamiltonian systems from reduction of an extended quasi-Poisson double of $U(n)$
• Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of compact Lie groups

Cited by in corpus (1)

• Integrable systems on multiplicative quiver varieties from cyclic quivers