The N-species integrable Volterra system as a maximally superintegrable Hamiltonian system
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 -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.
Cite
@article{arxiv.2505.09487,
title = {The N-species integrable Volterra system as a maximally superintegrable Hamiltonian system},
author = {Orlando Ragnisco and Federico Zullo},
journal= {arXiv preprint arXiv:2505.09487},
year = {2025}
}
Comments
21 pages, 6 figures. In the second verison some typos have been fixed and the bibliography has been rearranged. A typo in the abstract (metadata) has been fixed in the third version. The fourth version is in the OCNMP template format