Interesting facts: Hyperbolic and polynomial systems

In fast chaotic systems, also known as hyperbolic dynamical systems, divergence of nearby trajectories (i.e. the butterfly effect) at small scales occurs exponentially fast. In slowly chaotic systems, also known as parabolic systems, it is slower than exponential.

Difference between an exponential (fast divergence, e^t) and a parabolic (slow divergence, t²) function.