1 Gradient and Hamiltonian systems

• exposé

1 Gradient and Hamiltonian systems 1.1 Gradient systems These are quite special systems of ODEs, Hamiltonian ones arising in conserva- tive classical mechanics, and gradient systems, in some ways related to them, arise in a number of applications. They are certainly nongeneric, but in view of their origin, they are common. A system of the form X ′ = −∇V (X) (1) where V : Rn → R is, say, C∞, is called, for obvious reasons, a gradient system.

• various constants of motion of the approximation as candidates for lyapunov functions
• x∗
• initial condition x.
• phase portrait
• lyapunov function
• taylor approximation
• coordinates
• point
• system