The conditions of existence of first integrals and hamiltonian structures of Lotka-Volterra and Volterra systems |
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| Authors: | V. M. Dubovik A. G. Galperin V. S. Richvitsky S. K. Slepnyov |
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| Affiliation: | (1) Laboratory of High Energy, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia;(2) Laboratory Comp. Tech. Automat., Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia;(3) Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia |
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| Abstract: | A study of a certain subset of Volterra equations has revealed that some statements about time-independent constants of motion, Hamiltonian functions, and Poisson structure matrices appearing in the Lotka-Volterra equations, either regarded as proven or of the sort that could be proven, are not valid, in fact. Particular cases are given as examples to explain the reasons for the occurring phenomena. |
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