Locating a regular needle in a chaotic haystack, and conversely, using Lyapunov Weighted Dynamics

In many physical systems, dynamics is ruled by structures of atypical chaoticity. These structures may occupy a very small volume in phase space and can thus be very difficult to locate numerically. In this article, we review an algorithm, the Lyapunov Weighted Dynamics, which efficiently reveals trajectories of atypical chaoticity.