# On Some Properties and Symmetries of the 5-Dimensional Lorenz System

@article{Lzureanu2015OnSP, title={On Some Properties and Symmetries of the 5-Dimensional Lorenz System}, author={Cristian Lăzureanu and Tudor B{\^i}nzar}, journal={Mathematical Problems in Engineering}, year={2015}, volume={2015}, pages={1-7} }

The 5-dimensional Lorenz system for the gravity-wave activity is considered. Some stability problems and the existence of periodic orbits are studied. Also, a symplectic realization and some symmetries are given.

## 4 Citations

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The first integrals of system (1) are used and the theory of averaging of first order is used for studying the periodic solutions ofSystem (1), for more details on the averaging theory and its applications see [Buica & Llibre, 2004; Euzébio & L libre, 2014; L Libre & Vidal, 2015; Sanders et al., 2007; Verhulst, 1996] and the Appendix.

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This paper emphasizes some geometrical properties of the Maxwell–Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell–Bloch…

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