A poncelet map is an algebraic dynamical system defined by two conics[1] and the following procedure:
- Pick a starting point on the outer conic
- Draw a line from the point that is tangent to the inner conic
- This line intersects the outer conic at a new point
- Repeat the process from step 2
Given these are algebraic curves and these are relations of intersections and tangents, the map can be defined purely by algebraic equations and therefore is an algebraic dynamical system.[2]
One important property[clarification needed] is the Poncelet's closure theorem.[3]
References
- ↑ Cima, Anna; Gasull, Armengol; Mañosa, Víctor (13 December 2008). "On Poncelet's Maps".
- ↑ Dragovic, Vladimir; Radnovic, Milena; Birkhauser, Poncelet porism and beyond
- ↑ Levi, Mark; Tabachnikov, Serge. "The Poncelet grid and the billiard in an ellipse" (PDF).