Local limit theorem in deterministic systems

Abstract

We show that for every ergodic and aperiodic probability preserving system, there exists a $\mathbb{Z}$ valued, square integrable function $f$ such that the partial sums process of the time series ${\left\{f\circ T^i\right\}}_{i=0}^{\infty }$ satisfies the lattice local limit theorem.

17 pages