An exceprt from the article in Scilight https://aip.scitation.org/doi/10.1063/1.5128222
In the transition from mathematical billiards to physical billiards, where a ball goes from being a point particle to having a positive radius, it may seem intuitive to assume that no categorical difference exists between the two. A new proof-of-concept paper by Leonid Bunimovich says otherwise.
Bunimovich discovered as the radius of a physical billiard ball increases, the change in the behavior of the entire system is equivalent to modeling mathematical billiards with a smaller table. With increasing radius, the geometry of the system evolves. For instance, some parts of the table may become inaccessible to the ball. This results in a progression in the dynamics of the system between mathematical and physical cases, and it may become more or less chaotic with changing radius.
“Anything is possible,” said Bunimovich. “There are various types of transitions from order to chaos, and chaos to order.”
Article: “Physical versus mathematical billiards: From regular dynamics to chaos and back,” by L. A. Bunimovich, Chaos (2019). The article can be accessed at https://doi.org/10.1063/1.5122195.