Asymptotic Homotopical Complexity of an Infinite Sequence of Dispersing
$2D$ Billiards
Asymptotic Homotopical Complexity of an Infinite Sequence of Dispersing
$2D$ Billiards
We investigate the large scale chaotic, topological structure of the trajectories of an infinite sequence of dispersing, hence ergodic, $2D$ billiards with the configuration space $Q_n=\mathbb{T}^2 \setminus \bigcup_{i=0}^{n-1} D_i$, where the scatterers $D_i$ ($i=0,1,\dots,n-1$) are disks of radius $r<<1$ centered at the points $(i/n, 0)$ mod $\mathbb{Z}^2$. We get effective …