Limit theorems for dispersing billiards with cusps (Q652265)

This paper investigates certain probability limit theorems for dispersing billiards with cusps. Since these systems enjoy only polynomial decay of correlations of order \(1/n\), they exhibit weak and delicate statistical properties. The authors first prove the central limit theorem (CLT) for dynamical systems under fairly general conditions and then apply it specifically to dispersing billiards with cusps. The methods involved in the paper are demonstrated clearly, and involving a relatively new result on estimating decay rates of correlations for unbounded return time functions, which essentially follows from the growth lemma for systems with singularities. The authors prove a non-classical CLT, as well as a weak invariance principle.