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On the maximal superintegrability of strongly isochronous Hamiltonians
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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.
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Integrable systems from Poisson reductions of generalized Hamiltonian torus actions
Develops sufficient conditions for Poisson reduction of generalized Hamiltonian torus actions to preserve integrability and applies them to open problems on Lie group doubles and flat-connection moduli spaces.
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