Limit Theorems for Dispersing Billiards with Cusps

Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-classical central limit theorem holds, with a scaling factor of √ n logn replacing the standard √ n. We also derive the respective Weak Invariance Principle, and we identify the class of observables for which the classical CLT still holds.