Exploring self-intersected N-periodics in the elliptic billiard

Abstract

This is a continuation of our simulation-based investigation of N -periodic trajectories in the elliptic billiard. With a special focus on self-intersected trajectories we (i) describe new properties of N = 4 family, (ii) derive expressions for quantities recently shown to be conserved, and to support further experimentation, we (iii) derive explicit expressions for vertices and caustic semi-axes for several families. Finally, (iv) we include links to several animations of the phenomena.