Symmetries of some classes of dynamical systems

DOI

10.1080/14029251.2015.1033237How to use a DOI?

Keywords

symmetries; symplectic realization; Lie groups; Poisson structure; Hamiltonian dynamics; Lagrangian dynamics

Abstract

In this paper a three-dimensional system with five parameters is considered. For some particular values of these parameters, one finds known dynamical systems. The purpose of this work is to study some symmetries of the considered system, such as Lie-point symmetries, conformal symmetries, master symmetries and variational symmetries. In order to present these symmetries we give constants of motion. Using Lie group theory, Hamiltonian and bi-Hamiltonian structures are given. Also, symplectic realizations of Hamiltonian structures are presented. We have generalized some known results and we have established other new results. Our unitary presentation allows the study of these classes of dynamical systems from other points of view, e.g. stability problems, existence of periodic orbits, homoclinic and heteroclinic orbits.

Copyright

© 2015 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Cristian Lăzureanu
AU  - Tudor Bînzar
PY  - 2021
DA  - 2021/01/06
TI  - Symmetries of some classes of dynamical systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 265
EP  - 274
VL  - 22
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2015.1033237
DO  - 10.1080/14029251.2015.1033237
ID  - Lăzureanu2021
ER  -