A Central Limit Theorem for Periodic Orbits of Hyperbolic Flows
We consider a counting problem in the setting of hyperbolic dynamics. Let $ϕ_t : Λ\to Λ$ be a weak mixing hyperbolic flow. We count the proportion of prime periodic orbits of $ϕ_t$, with length less than $T$, that satisfy an averaging condition related to a Hölder continuous function $f: Λ\to \mathbb{R}$. We show, assuming an approximability condition on $ϕ$, that as $T \to \infty$, we obtain a central limit theorem.
math.DS↗