Two variations on the periscope theorem

22 Aug 2019  ·  Tabachnikov Serge ·

A spherical periscope in multi-dimensional space is a system of two ideal mirrors that reflect the rays emanating from a fixed point to the rays coming back to the same point, and a reversed periscope is a system of two mirrors that reflect the rays having a fixed direction to the rays having the opposite direction. We describe the local diffeomorphisms of the wave fronts (spherical, in the former, and flat, in the latter cases), induced by these 2-mirror systems...

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Differential Geometry Symplectic Geometry