Poncelet map

A poncelet map is an algebraic dynamical system defined by two conics¹ 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 is the Poncelet's closure theorem.³