Editing Lyapunov exponent (section)

==Basic properties==

If the system is conservative (i.e., there is no [[dissipation]]), a volume element of the phase space will stay the same along a trajectory. Thus the sum of all Lyapunov exponents must be zero. If the system is dissipative, the sum of Lyapunov exponents is negative.

If the system is a flow and the trajectory does not converge to a single point, one exponent is always zero—the Lyapunov exponent corresponding to the eigenvalue of <math>L</math> with an eigenvector in the direction of the flow.