On Birkhoff sums that satisfy no temporal distributional limit theorem for almost every irrational

Lorenz Frühwirth, Manuel Hauke

Dolgpoyat and Sarig showed that for any piecewise smooth function $f:\mathbb{T}\to \mathbb{R}$ and almost every pair $(\alpha ,x_0)\in \mathbb{T}\times \mathbb{T}$, $S_N(f,α,x_0) :=…