The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions.
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 X^*(t), perturb the system and write
X(t)=X^(t)+U(t),
(1)
where U(t) is the average deviation from the unperturbed trajectory at time t. In a chaotic region, the LCE sigma is independent of X^(0). It is given by the Oseledec theorem, which states that
sigma_i=lim_(t->infty)1/tln|U(t)|.
(2)
For an n-dimensional mapping, the Lyapunov characteristic exponents are given by
sigma_i=lim_(N->infty)ln|lambda_i(N)|
(3)
for i=1, ..., n, where lambda_i is the Lyapunov characteristic number.
