The remaining questions are short answer Do not write more t

The remaining questions are short answer. Do not write more than a sentence.

Suppose we are numerically integrating a chaotic system and two nearby initial conditions lead to very different trajectories on our first attempt. If we use small enough time steps, will the trajectories stay close together when we try again?

Solution

For any system, even for a chaotic one, if we use small enough time steps, then it will produce small changes in final conditions and hence, the trajectories will remain close if we try again.