Chaotic OrbitsTwo-Body ScatterClasses of TrajectoriesUnstable OrbitsThree-Body ScatterWada GeometryChaotic OrbitsChaotic OrbitsTwo-Body ScatterTwo-Body ScatterScattering disks are Scattering disks are massive.massive.Scattering particles can go Scattering particles can go through the gap or rebound.through the gap or rebound.•Sensitive to initial conditionsSensitive to initial conditionsParameterize the impact in Parameterize the impact in terms of two angles terms of two angles , , ..•Equivalent to selecting an Equivalent to selecting an initial vector.initial vector.Classes of TrajectoriesClasses of TrajectoriesStarting points that hit Starting points that hit multiple times map to other multiple times map to other points.points.•An orbit is a set of An orbit is a set of trajectories that have the trajectories that have the same outcome.same outcome.•Dashed orbits are Dashed orbits are trajectories that rebound.trajectories that rebound.•Solid orbits are trajectories Solid orbits are trajectories that pass through.that pass through.Unstable OrbitsUnstable OrbitsOrbits along curve S get Orbits along curve S get closer and closer to 0,0.closer and closer to 0,0.•Trapped trajectories that do Trapped trajectories that do not leave.not leave.•The point is a repellor to The point is a repellor to other trajectoriesother trajectoriesS acts as a separatrix S acts as a separatrix between trajectories that between trajectories that leave and those that leave and those that rebound.rebound.Three-Body ScatterThree-Body ScatterThree possible exit Three possible exit directions called basins.directions called basins.Trapped orbits exist as wellTrapped orbits exist as well•Two disk orbitsTwo disk orbits•Three disk orbitsThree disk orbitsMap describes a Wada basinMap describes a Wada basin•Initial position and angleInitial position and angle•Forms a fractal mapForms a fractal map•Physical realization in opticsPhysical realization in opticsWada GeometryWada
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