PHYSICS

Nonlinear Dynamics

Nonlinear Dynamics

The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions. To examine the behavior of an orbit around a point , perturb the system and write

(1)

where is the average deviation from the unperturbed trajectory at time . In a chaotic region, the LCE is independent of . It is given by the Oseledec theorem, which states that

(2)

For an -dimensional mapping, the Lyapunov characteristic exponents are given by

(3)

for , ..., , where is the Lyapunov characteristic number.

One Lyapunov characteristic exponent is always 0, since there is never any ...