Poncelet map

A poncelet map is an algebraic dynamical system defined by two conics[1] and the following procedure:

A poncelet map is an algebraic dynamical system defined by two conics[1] and the following procedure:

  1. Pick a starting point on the outer conic
  2. Draw a line from the point that is tangent to the inner conic
  3. This line intersects the outer conic at a new point
  4. 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

  1. ^ Cima, Anna; Gasull, Armengol; Mañosa, Víctor (13 December 2008). "On Poncelet's Maps".
  2. ^ Dragovic, Vladimir; Radnovic, Milena; Birkhauser, Poncelet porism and beyond
  3. ^ Levi, Mark; Tabachnikov, Serge. "The Poncelet grid and the billiard in an ellipse" (PDF).

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