Consider Birkhoff sums Sn=k<nvTk where T is a billiard with a flat cusp and stability index α=32, and v is an observable given by v(r,φ)=cos(5φ). Here φ is the post-collisional angle between particle's velocity and the normal to the boundary.

We choose a random initial condition and plot the process Wn(t), 0t1, given by Wn(t)=1n2/3Snt. We send n and animate the graph. We also plot in light grey the graphs of tct2/3 with a few different values of c.

Refresh the page to restart with a new initial contition.