2024/10/23 by Gogolev, Andrey, Keck, Levi, Lewis, Kevin
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2410.17985
We introduce a new class of billiard-like system, ``bouncing outer billiards" which are 3-dimensional cousins of outer billiards of Neumann and Moser. We prove that bouncing outer billiard on a smooth convex body has at least four 1-parameter families of fixed points. We also fully describe dynamics of bouncing outer billiard on a line segment. Finally we carry out numerical experiments suggesting very complicated (non-ergodic) behavior for several shapes including the square and an ellipse.