Comptes Rendus
Dynamical Systems/Mathematical Physics
On the symmetries of a Rikitake type system
[Sur les symétries dʼun système de type Rikitake]
Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 529-533.

On présente une réalisation symplectique et certaines symétries dʼun système de type Rikitake.

A symplectic realization and some symmetries of a Rikitake type system are presented.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.04.016

Cristian Lăzureanu 1 ; Tudor Bînzar 1

1 Department of Mathematics, “Politehnica” University of Timişoara, Piaţa Victoriei No. 2, Timişoara 300006, Romania
@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},
     publisher = {Elsevier},
     volume = {350},
     number = {9-10},
     year = {2012},
     doi = {10.1016/j.crma.2012.04.016},
     language = {en},
}
TY  - JOUR
AU  - Cristian Lăzureanu
AU  - Tudor Bînzar
TI  - On the symmetries of a Rikitake type system
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 529
EP  - 533
VL  - 350
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crma.2012.04.016
LA  - en
ID  - CRMATH_2012__350_9-10_529_0
ER  - 
%0 Journal Article
%A Cristian Lăzureanu
%A Tudor Bînzar
%T On the symmetries of a Rikitake type system
%J Comptes Rendus. Mathématique
%D 2012
%P 529-533
%V 350
%N 9-10
%I Elsevier
%R 10.1016/j.crma.2012.04.016
%G en
%F CRMATH_2012__350_9-10_529_0
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.016/

[1] G.W. Bluman; S. Kumei Symmetries and Differential Equations, Appl. Math. Sci., vol. 81, Springer-Verlag, New York, 1989

[2] P.A. Damianou Multiple Hamiltonian structures for Toda systems of type A–B–C, Regul. Chaotic Dyn., Volume 5 (2000) no. 1, pp. 17-32

[3] P.A. Damianou; P.G. Paschali Symmetries of Maxwell–Bloch equations, J. Nonlinear Math. Phys., Volume 2 (1995) no. 3–4, pp. 269-278

[4] A.S. Fokas; B. Fuchssteiner The Hierarchy of the Benjamin–Ono equations, Phys. Lett. A, Volume 86 (1981), pp. 341-345

[5] B. Fuchssteiner Mastersymmetries and higher order time-dependent symmetries and conserved densities of nonlinear evolution equations, Progr. Theoret. Phys., Volume 70 (1983), pp. 1508-1522

[6] P. Libermann; C.-M. Marle Symplectic Geometry and Analytical Mechanics, D. Reidel, Dordrecht, 1987

[7] J. Marsden; A. Weinstein Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids, Phys. D, Volume 7 (1983), pp. 305-323

[8] P.J. Olver Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1986

[9] T. Rikitake Oscillations of a system of disk dynamos, Proc. Cambridge Philos. Soc., Volume 54 (1958), pp. 89-105

[10] W.-H. Steeb 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] R.M. Tudoran; A. Aron; Ş. Nicoară On a Hamiltonian version of the Rikitake system, SIAM J. Appl. Dyn. Syst., Volume 8 (2009) no. 1, pp. 454-479

  • Remus-Daniel Ene; Nicolina Pop; Rodica Badarau Symmetries and Closed-Form Solutions for Some Classes of Dynamical Systems, Symmetry, Volume 17 (2025) no. 4, p. 546 | DOI:10.3390/sym17040546
  • Angel Ballesteros; Alfonso Blasco; Ivan Gutierrez-Sagredo Integrable deformations of Rikitake systems, Lie bialgebras and bi-Hamiltonian structures, Communications in Nonlinear Science and Numerical Simulation, Volume 137 (2024), p. 108167 | DOI:10.1016/j.cnsns.2024.108167
  • Remus-Daniel Ene; Nicolina Pop Semi-Analytical Closed-Form Solutions for the Rikitake-Type System through the Optimal Homotopy Perturbation Method, Mathematics, Volume 11 (2023) no. 14, p. 3078 | DOI:10.3390/math11143078
  • Remus-Daniel Ene; Nicolina Pop; Marioara Lapadat; Luisa Dungan Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method, Mathematics, Volume 10 (2022) no. 21, p. 4118 | DOI:10.3390/math10214118
  • Remus-Daniel Ene; Nicolina Pop; Marioara Lapadat Approximate Closed-Form Solutions for the Rabinovich System via the Optimal Auxiliary Functions Method, Symmetry, Volume 14 (2022) no. 10, p. 2185 | DOI:10.3390/sym14102185
  • Yanling Wang; Tengfei Lei; Xin Zhang; Chunbiao Li; Sajad Jafari Hyperchaotic Oscillation in the Deformed Rikitake Two-Disc Dynamo System Induced by Memory Effect, Complexity, Volume 2020 (2020), p. 1 | DOI:10.1155/2020/8418041
  • Kaiyin Huang; Shaoyun Shi; Zhiguo Xu Integrable deformations, bi-Hamiltonian structures and nonintegrability of a generalized Rikitake system, International Journal of Geometric Methods in Modern Physics, Volume 16 (2019) no. 04, p. 1950059 | DOI:10.1142/s0219887819500592
  • Cristian Lazureanu; Ciprian Hedrea; Camelia Petrisor, 2018 International Conference on Applied Mathematics Computer Science (ICAMCS) (2018), p. 1 | DOI:10.1109/icamcs46079.2018.000-6
  • Cristian Lăzureanu Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System, Advances in Mathematical Physics, Volume 2017 (2017), p. 1 | DOI:10.1155/2017/4596951
  • Gheorghe Tigan Degenerate with respect to parameters fold-Hopf bifurcations, Discrete Continuous Dynamical Systems - A, Volume 37 (2017) no. 4, p. 2115 | DOI:10.3934/dcds.2017091
  • Ioan Caşu Symmetries of the Maxwell-Bloch equations with the rotating wave approximation, Regular and Chaotic Dynamics, Volume 19 (2014) no. 5, p. 548 | DOI:10.1134/s1560354714050037

Cité par 11 documents. Sources : Crossref

Commentaires - Politique


Il n'y a aucun commentaire pour cet article. Soyez le premier à écrire un commentaire !


Publier un nouveau commentaire:

Publier une nouvelle réponse: