A symplectic realization and some symmetries of a Rikitake type system are presented.
On présente une réalisation symplectique et certaines symétries dʼun système de type Rikitake.
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Cristian Lăzureanu 1; Tudor Bînzar 1
@article{CRMATH_2012__350_9-10_529_0,
author = {Cristian L\u{a}zureanu and Tudor B{\^\i}nzar},
title = {On the symmetries of a {Rikitake} type system},
journal = {Comptes Rendus. Math\'ematique},
pages = {529--533},
year = {2012},
publisher = {Elsevier},
volume = {350},
number = {9-10},
doi = {10.1016/j.crma.2012.04.016},
language = {en},
}
Cristian Lăzureanu; Tudor Bînzar. On the symmetries of a Rikitake type system. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 529-533. doi: 10.1016/j.crma.2012.04.016
[1] Symmetries and Differential Equations, Appl. Math. Sci., vol. 81, Springer-Verlag, New York, 1989
[2] Multiple Hamiltonian structures for Toda systems of type A–B–C, Regul. Chaotic Dyn., Volume 5 (2000) no. 1, pp. 17-32
[3] Symmetries of Maxwell–Bloch equations, J. Nonlinear Math. Phys., Volume 2 (1995) no. 3–4, pp. 269-278
[4] The Hierarchy of the Benjamin–Ono equations, Phys. Lett. A, Volume 86 (1981), pp. 341-345
[5] Mastersymmetries and higher order time-dependent symmetries and conserved densities of nonlinear evolution equations, Progr. Theoret. Phys., Volume 70 (1983), pp. 1508-1522
[6] Symplectic Geometry and Analytical Mechanics, D. Reidel, Dordrecht, 1987
[7] Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids, Phys. D, Volume 7 (1983), pp. 305-323
[8] Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1986
[9] Oscillations of a system of disk dynamos, Proc. Cambridge Philos. Soc., Volume 54 (1958), pp. 89-105
[10] Continuous symmetries of the Lorenz model and the Rikitake two-disc dynamo system, J. Phys. A: Math. Gen., Volume 15 (1982), pp. 389-390
[11] On a Hamiltonian version of the Rikitake system, SIAM J. Appl. Dyn. Syst., Volume 8 (2009) no. 1, pp. 454-479
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