Lyapunov exponent

Rate of separation of infinitesimally close trajectories

In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the exponential rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories in phase space with initial separation vector δ 0 {\displaystyle {\boldsymbol {\delta }}_{0}} diverge (provided that the divergence can be treated within the linearized approximation) at a rate given by | δ ( t) | ≈ e λ t | δ 0 | {\displaystyle |{\boldsymbol {\delta }}(t)|\approx e^{\lambda t}|{\boldsymbol {\delta }}_{0}|} where λ {\displaystyle \lambda } is the Lyapunov exponent. The rate of separation can be different for different orientations of initial separation vector.

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