Multidimensional local limit theorem in deterministic systems and an application to non-convergence of polynomial multiple averages

Zemer Kosloff, Shrey Sanadhya

We show that for every ergodic and aperiodic probability preserving system $(X,\mathcal{B},m,T)$, there exists $f:X\to {\mathbb{Z}}^d$, whose corresponding cocycle satisfies the $d$-…