= Geodesic scattering relation
{title2=$\alpha(x,v)=(\gamma(\tau),\dot\gamma(\tau))$}
= Scattering relation
{synonym}
For an inward unit boundary vector, the geodesic scattering relation returns the next boundary point and its outgoing unit velocity. On outward vectors it can be extended using the first backward exit, giving an involution on the full boundary unit bundle, with tangential vectors fixed. Exit time is separate lens data; on a simple manifold it equals boundary distance between the endpoint pair.
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