Limit Theorems for Self-Intersecting Trajectories in $$\mathbb {Z}$$ -Extensions

Abstract

We investigate the asymptotic properties of the self-intersection numbers for \(\mathbb {Z}\)-extensions of chaotic dynamical systems, including the \(\mathbb {Z}\)-periodic Lorentz gas and the geodesic flow on a \(\mathbb {Z}\)-cover of a negatively curved compact surface. We establish a functional limit theorem.