Dynamical system

Conservative system

A conservative system is a system for which all infinitesimal volumes remain the same, #m/def/dynamics i.e. $t r (𝐷 𝑓 (𝐱)) = 0$ everywhere for a differential system or $d e t (𝐷 𝑓 (𝐱)) = 0$ everwhere for an iterated map.

Properties

Often have homoclinic orbits
Never have stable fixed points

Example

Ideal pendulum — centres (at bottom) and saddles (at top), (homoclinic?) saddles form separatrix between oscillation and rotation.

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