  The transition from order to chaos has been a major subject of research since
the work of Poincare, as it is relevant in areas ranging from the foundations
of statistical physics to the stability of the solar system. Along this
transition, atypical structures like the first chaotic regions to appear, or
the last regular islands to survive, play a crucial role in many physical
situations. For instance, resonances and separatrices determine the fate of
planetary systems, and localised objects like solitons and breathers provide
mechanisms of energy transport in nonlinear systems such as Bose-Einstein
condensates and biological molecules. Unfortunately, despite the fundamental
progress made in the last years, most of the numerical methods to locate these
'rare' trajectories are confined to low-dimensional or toy models, while the
realms of statistical physics, chemical reactions, or astronomy are still hard
to reach. Here we implement an efficient method that allows one to work in
higher dimensions by selecting trajectories with unusual chaoticity. As an
example, we study the Fermi-Pasta-Ulam nonlinear chain in equilibrium and show
that the algorithm rapidly singles out the soliton solutions when searching for
trajectories with low level of chaoticity, and chaotic-breathers in the
opposite situation. We expect the scheme to have natural applications in
celestial mechanics and turbulence, where it can readily be combined with
existing numerical methods
