scholarly journals Dynamical systems and Poisson structures

2009 ◽  
Vol 50 (11) ◽  
pp. 112703 ◽  
Author(s):  
Metin Gürses ◽  
Gusein Sh. Guseinov ◽  
Kostyantyn Zheltukhin
Keyword(s):  
Dynamical Systems ◽  
Poisson Structures

Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems

2014 ◽  
Vol 6 (01) ◽  
pp. 87-106
Author(s):  
Xueyang Li ◽  
Aiguo Xiao ◽  
Dongling Wang
Keyword(s):  
Dynamical Systems ◽  
Hamiltonian Systems ◽  
Generating Function ◽  
Poisson Structure ◽  
Poisson Structures ◽  
Volterra Systems

AbstractThe generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices. In this paper, we extend these results and present the generating function methods preserving the Poisson structures for generalized Hamiltonian systems with general variable Poisson-structure matrices. In particular, some obtained Poisson schemes are applied efficiently to some dynamical systems which can be written into generalized Hamiltonian systems (such as generalized Lotka-Volterra systems, Robbins equations and so on).

scholarly journals ON PLANAR AND NON-PLANAR ISOCHRONOUS SYSTEMS AND POISSON STRUCTURES

2010 ◽  
Vol 07 (07) ◽  
pp. 1115-1131 ◽  
Author(s):  
PARTHA GUHA ◽  
A. GHOSE CHOUDHURY
Keyword(s):  
Dynamical Systems ◽  
Poisson Structure ◽  
Poisson Structures ◽  
Isochronous Systems

We construct certain new classes of isochronous dynamical systems based on the recent constructions of Calogero and Leyvraz. We show how a Poisson structure can be ascribed to such equations in ℝ3 and indicate their connection with the Nambu structures.

scholarly journals DYNAMICAL ASPECTS OF LIE-POISSON STRUCTURES

1993 ◽  
Vol 08 (31) ◽  
pp. 2973-2987 ◽  
Author(s):  
F. LIZZI ◽  
G. MARMO ◽  
G. SPARANO ◽  
P. VITALE
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Poisson Bracket ◽  
Lie Groups ◽  
Hamiltonian Systems ◽  
Quantum Groups ◽  
Equations Of Motion ◽  
Poisson Structures ◽  
Dimensional Phase Space ◽  
Deformation Procedure

Quantum groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems which are associated with this bracket. We look at SU(2) and SU(1, 1), as submanifolds of a four-dimensional phase space with constraints, and deal with two classes of problems. In the first set of examples we consider some Hamiltonian systems associated with Lie-Poisson structures and we investigate the equations of motion. In the second set of examples we consider systems which preserve the chosen bracket, but are dissipative. However in this approach, they survive the quantization procedure.

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