page_title: Chaotic scattering
section_title: An experimental system and the stable manifold
hierarchical_section_title: Chaotic scattering / An experimental system and the stable manifold
caption_attribution_description: English: Gaspard-Rice scattering system being tested experimentally with coloured strips of cardboard: the basins of attraction are projected onto the impact-parameter space.
context_page_description: Chaotic scattering is a branch of chaos theory dealing with scattering systems displaying a strong sensitivity to initial conditions. In a classical scattering system there will be one or more impact parameters, b, in which a particle is sent into the scatterer. This gives rise to one or more exit parameters, y, as the particle exits towards infinity. While the particle is traversing the system, there may also be a delay time, T—the time it takes for the particle to exit the system—in addition to the distance travelled, s, which in certain systems, i.e., "billiard-like" systems in which the particle undergoes lossless collisions with hard, fixed objects, the two will be equivalent—see below. In a chaotic scattering system, a minute change in the impact parameter, may give rise to a very large change in the exit parameters.
context_section_description: Figure 4 shows an experimental realization of the
  Gaspard–Rice system using a laser instead of a point particle.
  As anyone who's actually tried this knows, this is not a very effective
  method of testing the system—the laser beam gets scattered in every
  direction.  As shown by Sweet, Ott and Yorke,
   
  a more effective method is to direct coloured light through the gaps 
  between the discs (or in this case, tape coloured strips of paper across pairs of cylinders)
  and view the reflections through an open gap.
  The result is a complex pattern of stripes of alternating colour, as
  shown below, seen more clearly in the simulated version below that.
  Figures 5 and 6 show the basins of attraction for each
  impact parameter, b, that is, for a given value of b, through which gap
  does the particle exit?  The basin boundaries form a Cantor set and
  represent members of the stable manifold: trajectories that, once started, never
  exit the system.
caption: Fig. 5: An experimental Gaspard–Rice scattering system showing basins of attraction.[4]
exif: {}