# Lyapunov Exponents - Why do the small perturbation of a trajectory and the initial trajectory separate exponentially quickly?

I am writing a report about chaos theory and I am currently studying Lyapunov exponents, I understand that a small change between trajectories will separate exponentially quickly by the following equation.

$$|\delta(t)|\approx|\delta_0|e^{\lambda t}$$

I am interested to find out where this approximation arises from. I hope somebody could be of help.

• – Wrzlprmft Mar 27 at 17:40