Internal-wave ray return map ($x_{n+1}=R(x_n)$)

Map one boundary intersection of an internal-wave ray to the next intersection with the same boundary after a specified reflection itinerary. A periodic ray is a fixed point. Linear contraction, $|R^{\prime }|<1$, gives an internal-wave attractor; the reversed itinerary, when invertible, has reciprocal multiplier and is locally repelling.