2021/03/28 by Oğul Esen, Esen, Oğul, Partha Guha +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · doi:10.48550/arxiv.2103.15058
We examine 3D flows \mathbfx=v(\bf x) admitting vector identity Mv = ∇ × A for a multiplier M and a potential field A. It is established that, for those systems, one can complete the vector field v into a basis fitting an \mathfraksl(2)-algebra. Accordingly, in terms of covariant quantities, the structure equations determine a set of equations in Maurer-Cartan form. This realization permits one to obtain the potential field as well as to investigate the (bi-)Hamiltonian character of the system. The latter occurs if the system has a time-independent first integral. In order to exhibit the theoretical results on some concrete cases, three examples are provided, namely the Gulliot system, a system with a non-integrable potential, and the Darboux-Halphen system in symmetric polynomials.