A Berry Esseen result for the billiard transformation

Françoise Pene (1)

1 LM - Laboratoire de mathématiques de Brest

We consider billiard systems in the two dimensional torus with convex obstacles. In this paper, we prove a rate of convergence in $n^{-{1\over 2}}$ in the central limit theorem in the case of the billiard transformation. For one-dimensional functions, we control the maximal decay between the distribution functions.For multi-dimensional functions, we control the Prokhorov metric.

Domaines: Systèmes dynamiques [math.DS]

Françoise Pene. A Berry Esseen result for the billiard transformation. 2007. ⟨hal-01101281⟩