Complete integrability of vector fields inRN

Aziz, 2012, Local integrability and linearizability of three–dimensional Lotka-Volterra systems, Appl. Math. Comput., 219, 4067, 10.1016/j.amc.2012.10.051 Blé, 2013, Integrability and global dynamics of the May–Leonard model, Nonlinear Anal., Real World Appl., 14, 280, 10.1016/j.nonrwa.2012.06.004 Cairó, 2000, Darboux integrability for the 3–dimensional Lotka–Volterra systems, J. Phys. A, Math. Gen., 33, 2395, 10.1088/0305-4470/33/12/307 Crespo, 2016, Poisson and integrable systems through the Nambu bracket and its Jacobi multiplier, J. Geom. Mech., 2, 169 Chi, 1998, On the asymmetric May–Leonard model of three competing species, SIAM J. Appl. Math., 58, 221, 10.1137/S0036139994272060 Clebsch, 1859, Ueber die Integration der hydrodynamischen Gleichungen, J. Reine Angew. Math., 56, 1 Erugin, 1952, Construction of the whole set of differential equations having a given integral curve, Akad. Nauk SSSR. Prikl. Mat. Meh., 16, 659 Filippov, 1998, On the n–Lie algebras of Jacobians, Sib. Mat. Zh., 3, 660 Galliulin, 1997, Analytical dynamics, Helmholtz, Kirchhoff and Nambu systems, Usp. Fiz. Nauk Galiullin, 1984 Galiullin, 1994, Investigations on the analytical design of the programmed-motion systems, Vestnik RUDN, Ser. Applied Math., 98, 6 Goriely, 2001, Integrability and Nonintegrability of Dynamical Systems, vol. 19 Llibre, 2016, Inverse Problems in Ordinary Differential Equations and Applications, vol. 313 Llibre, 2014, Inverse problems in ordinary differential equations. Applications to mechanics, J. Dyn. Differ. Equ., 26, 529, 10.1007/s10884-014-9390-1 Muxarliamov, 1967, On the inverse problem in the qualitative theory of ordinary differential equations, Differ. Uravn., 10, 1673 Nambu, 1973, Generalized Hamiltonian dynamics, Phys. Rev. D, 7, 2405, 10.1103/PhysRevD.7.2405 Rutherford, 1989 Sadovskaia, 2002 Tudoran, 2012, A normal form of completely integrable systems, J. Geom. Phys., 62, 1167, 10.1016/j.geomphys.2011.12.003 Whittaker, 1944