next up previous

1 Flows vs. Maps     continued...

The system of equations in (1) is an example of a flow, which gives rise to a continuous evolution of ``field lines'' in the n-dimensional space (sometimes called the ``phase space'') [2]. We say that the flow is conservative if the volume in phase space remains constant with time. If the volume decreases with time, there is a damping effect in the dynamics, and we refer to the resulting flow as dissipative. (A frictional force in a mechanical system gives rise to dissipation, as does a resistor in an electrical system.)

Also, it is sometimes convenient to write Eq. (1) in column vector form

where