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Dynamical systems and Poisson structures
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Date
2009-11-01
Author
Guerses, Metin
Guseinov, Gusein Sh
Zheltukhın, Kostyantyn
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We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender et al. [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that all dynamical systems in R-n are locally (n-1)-Hamiltonian. We give also an algorithm, similar to the case in R-3, to construct a rank two Poisson structure of dynamical systems in R-n. We give a classification of the dynamical systems with respect to the invariant functions of the vector field (X) over right arrow and show that all autonomous dynamical systems in R-n are super-integrable. (C) 2009 American Institute of Physics. [doi:10.1063/1.3257919]
Subject Keywords
Mathematical Physics
,
Statistical and Nonlinear Physics
URI
https://hdl.handle.net/11511/37377
Journal
JOURNAL OF MATHEMATICAL PHYSICS
DOI
https://doi.org/10.1063/1.3257919
Collections
Department of Mathematics, Article
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M. Guerses, G. S. Guseinov, and K. Zheltukhın, “Dynamical systems and Poisson structures,”
JOURNAL OF MATHEMATICAL PHYSICS
, pp. 0–0, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37377.