Lyapunov Exponents 6.1 Stretch, Strain and Twirl

L et us apply our newly acquired tools to the fundamental diagnostics in dynamics: Is a given system ‘chaotic’? And if so, how chaotic? If all points in example 2.3 a neighborhood of a trajectory converge toward the same orbit, the attractor is a fixed point or a limit cycle. However, if the attractor is strange, any two section 1.3.1 trajectories x(t) = f (x0) and x(t)+δx(t) = f (x0 + δx0) that start out very close to remark 6.1 each other separate exponentially with time, and in a finite time their separation attains the size of the accessible state space.