Chaos in Billiard Balls
This gives a phase space plot for two slopes for two consecutive collisions vs. distance between the collisions for thousand randomly selected points. What this graph shows is that basically the system is a two dimensional system (meaning it has only two independent variables) what can't be seen here is that instead of only one surface it is composed of two surface that intersect along a curve. The other graph is what is called the lyapunov exponent vs. a parameter that determine ellipticity of the ellipse. It can be observed that lyapunov exponent is around to 0.011 value with occasional variation. This basically tells about the aperiodicity of the system, and that it is not chaotic.
The python files and report could be found at files.
This is one of the other Mathematical modeling problem. In this problem what we assume is that a ball is let to bounce inside a board( which is assumed to be a elliptic board). It is known that if the board is make of two parallel edge connected by each other by half circles, then there is possibility of chaos in the time series(see Dynamic Billiard). What this study is done on elliptic board, it can be shown that the result is actually quasi-periodic and not chaotic.