A unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions and/or first integrals
McLachlan, Robert I ; Quispel, GRW ; Robidoux, Nicolas
arXiv, 9805021 / Harvested from arXiv
Text on arXiv
Systems with a first integral (i.e., constant of motion) or a Lyapunov function can be written as ``linear-gradient systems'' $\dot x= L(x)\nabla V(x)$ for an appropriate matrix function $L$, with a generalization to several integrals or Lyapunov functions. The discrete-time analogue, $\Delta x/\Delta t = L \bar\nabla V$ where $\bar\nabla$ is a ``discrete gradient,'' preserves $V$ as an integral or Lyapunov function, respectively.
Publié le : 1998-05-24
Classification:  Mathematical Physics,  Mathematics - Dynamical Systems,  Mathematics - Numerical Analysis 
@article{9805021,
     author = {McLachlan, Robert I and Quispel, GRW and Robidoux, Nicolas},
     title = {A unified approach to Hamiltonian systems, Poisson systems, gradient
  systems, and systems with Lyapunov functions and/or first integrals},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9805021}
}

McLachlan, Robert I; Quispel, GRW; Robidoux, Nicolas. A unified approach to Hamiltonian systems, Poisson systems, gradient
  systems, and systems with Lyapunov functions and/or first integrals. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9805021/