A unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions and/or first integrals

Abstract

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.

13 pages, no figures, REVTEX source

References in corpus (1)

• On Foundation of the Generalized Nambu Mechanics

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