Problem dossier · Dynamics & Analysis
Outer billiards unboundedness
For which convex shapes does the outer (dual) billiard map admit unbounded orbits? Moser asked whether orbits can escape to infinity at all.
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Status
Schwartz (2007) proved unbounded orbits exist for the Penrose kite; boundedness for general polygons (e.g. all quadrilaterals, generic polygons) remains open.
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The Angle of Attack
Simulate orbits for families of polygons with exact rational arithmetic; map the return dynamics and hunt escape channels beyond the known kite cases.
Tags: billiards · dynamics · unbounded orbits · simulation
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The Lab
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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