Arieşanu, Camelia Pop A Hamilton-Poisson model of the Chen-Lee system. (English) Zbl 1255.34013 J. Appl. Math. 2012, Article ID 484028, 11 p. (2012). Summary: We present some dynamical and geometrical properties of the Chen-Lee system from the point of view of Poisson geometry. MSC: 34A26 Geometric methods in ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 34D20 Stability of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations PDF BibTeX XML Cite \textit{C. P. Arieşanu}, J. Appl. Math. 2012, Article ID 484028, 11 p. (2012; Zbl 1255.34013) Full Text: DOI OpenURL References: [1] H.-K. Chen and C.-I. Lee, “Anti-control of chaos in rigid body motion,” Chaos, Solitons & Fractals, vol. 21, no. 4, pp. 957-965, 2004. · Zbl 1046.70005 [2] T. Wang, K. Wang, and N. Jia, “Chaos control and hybrid projective synchronization of a novel chaotic system,” Mathematical Problems in Engineering, vol. 2011, Article ID 452671, 13 pages, 2011. · Zbl 1213.34077 [3] J.-M. Ginoux and B. Rossetto, “Differential geometry and mechanics: applications to chaotic dynamical systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 4, pp. 887-910, 2006. · Zbl 1111.37021 [4] M. W. Hirsch, S. Smale, and R. L. Devaney, Differential Equations, Dynamical Systems and an Introduction to Chaos, Pure and Applied Mathematics (Amsterdam), Academic Press, Amsterdam, The Netherlands, 2003. · Zbl 1239.37001 [5] G.-M. Marle, “Symplectic manifolds, dynamical groups, and Hamiltonian mechanics,” in Differential Geometry and Relativity, M. Cahen and M. Flato, Eds., Reidel, Dordrecht, The Netherlands, 1976. · Zbl 0369.53042 [6] F. Haas and J. Goedert, “On the generalized Hamiltonian structure of 3D dynamical systems,” Physics Letters A, vol. 199, no. 3-4, pp. 173-179, 1995. · Zbl 1020.35533 [7] M. Puta, “Lie-Trotter formula and Poisson dynamics,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 9, no. 3, pp. 555-559, 1999. · Zbl 0970.37063 [8] M. Puta, Hamiltonian Systems and Geometric Quantization, Mathematics and Its Applications, vol. 260, Springer, Berlin, Germany, 1993. · Zbl 0795.70001 [9] P. Birtea, M. Puta, and R. M. Tudoran, “Periodic orbits in the case of a zero eigenvalue,” Comptes rendus de l’Académie des sciences. Série 1, Mathématique, vol. 344, no. 12, pp. 779-784, 2007. · Zbl 1131.34034 [10] W. Kahan, Unconventional Numerical Methods for Trajectory Calculation, Unpublished Lecture Notes, 1993. [11] R. M. Tudoran, A. Aron, and S. Nicoar\ua, “On a Hamiltonian version of the Rikitake system,” SIAM Journal on Applied Dynamical Systems, vol. 8, no. 1, pp. 454-479, 2009. · Zbl 1159.70356 [12] C. Pop, C. Petri\csor, and D. B\ual\ua, “Hamilton-Poisson realizations for the Lü system,” Mathematical Problems in Engineering, vol. 2011, Article ID 842325, 13 pages, 2011. · Zbl 1223.34067 [13] C. Pop Ariesanu, “Numerical integration and stability problems in the study of Lorenz system,” Acta Technica Napocensis, vol. 2, no. 54, pp. 333-339, 2011. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.