  Many authors consider an important mark of chaos to be trajectories issuing from nearby points diverging from one another exponentially quickly. However, it is also possible for trajectory divergence to be faster than exponential. Take Poincaré’s example of a molecule in a gas of \(N\) molecules. If this molecule suffered the slightest of deviations from its initial starting point and you compared the molecule’s trajectories from these two slightly different starting points, the resulting trajectories would diverge at a geometric rate, to the \(n\)th power, due to the \(n\) subsequent collisions, each being different than what it would have been had there been no slight change in the initial condition.