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

Robert I McLachlan, GRW Quispel, Nicolas Robidoux

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 fu…