Stable CLT for deterministic systems

Abstract

We show that for every ergodic and aperiodic probability preserving transformation and $\alpha \in (0,2)$ there exists a function whose associated time series is in the standard domain of attraction of a non-degenerate symmetric $\alpha$-stable distribution.

17 pages, 0 figures Version 2: restructured the paper in order to improve the presentation and adjusted the proofs accordingly