… the boundary of the table has equation

((x/a)^(2))^q + ((y/b)^(2))^q = 1 ;

& if q = 1 we have the usual ellipse, & if q>1 a 'plump' super-ellipse, & if q<1 a 'gaunt' super-ellipse; & if a plump superellipse is the boundary of a billiard table (mathematically ideal: perfectly elastic & specular rebounding @ the boundary), then within certain regions of the parameter-space - characterised by q being sufficiently large @ given value of a:b - the paths become chaotic.

I first found-out about this particular transition to chaos a very long time ago, & tested it with a little computer program, finding that it seemed to be true … but I've longsince lost what I found-out about it from , & haven't been able either to refind it, or find something new about the phenomenon, since. I've put a query in @

#####r/AskMath

about it … but nothing's shown-up. So I'm figuring that maybe someone @ this channel knows something about it.

And, ofcourse, the video showcases the phenomenon beautifully !