Phys. Rev. Lett. 81, 2399–2403 (1998)Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First IntegralsReceived 21 April 1998; published in the issue dated 21 September 1998 We show that systems with a first integral (i.e., a constant of motion) or a Lyapunov function can be written as “linear-gradient systems,” ẋ = L(x)▽V(x), for an appropriate matrix function L, with a generalization to several integrals or Lyapunov functions. The discrete-time analog, Δx/Δt = L▽̅ V, where ▽̅ is a “discrete gradient,” preserves V as an integral or Lyapunov function, respectively. © 1998 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.81.2399
DOI:
10.1103/PhysRevLett.81.2399
PACS:
03.20.+i, 02.60.Lj
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