  In this paper we study convex caustics in Minkowski billiards. We show that
for the Euclidean billiard dynamics in a planar smooth centrally symmetric and
strictly convex body $K$, for every convex caustic which $K$ possesses, the
"dual" billiard dynamics in which the table is the Euclidean unit disk and the
geometry that governs the motion is induced by the body $K$, possesses a dual
convex caustic. Such a pair of caustics is dual in a strong sense, and in
particular they have the same perimeter, Lazutkin parameter (both measured with
respect to the corresponding geometries), and rotation number. We show moreover
that for general Minkowski billiards this phenomenon fails, and one can
construct a smooth caustic in a Minkowski billiard table which possesses no
dual convex caustic.
