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The N-species integrable Volterra system as a maximally superintegrable Hamiltonian system
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abstract
The results presented in this paper are a natural development of those described in the paper {\it The Volterra Integrable case. Novel analytical and numerical results} (OCNMP Vol.4 (2024) pp 188-211), where the authors reconsidered the integrable case of the Hamiltonian $N$-species Lotka-Volterra system, introduced by Vito Volterra in 1937. There, an alternative approach for constructing the integrals of motion has been proposed, and compared with the old Volterra approach. Here we go beyond, and show that in fact the model introduced by Volterra and studied by us is not just integrable, but is maximally superintegrable and reducible to a system with only one degree of freedom regardless the number of species considered. We present both analytical and numerical results.
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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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