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), where U(t) is the average deviation from the unperturbed trajectory at time t. In a chaotic region, the LCE σ is independent of X^*(0). It is given by the Oseledec theorem, which states that σ_i = lim_(t->∞) 1/t ln left bracketing bar U(t) right bracketing bar .

chaos | Hamiltonian system | Lyapunov characteristic number | Oseledec theorem