3 problems

Let $f\colon X\to X$ be a nonuniformly expanding map with reference measure $m$, return time $\tau$, and physical invariant measure $\mu$. Let $\varphi\colon X\to\mathbb{R}$ be Höl…

Let $(X_n)_{n\geq 0}$ be a random process satisfying an almost sure invariance principle, meaning that, possibly after enlarging the probability space, there is a Brownian motion…

The discussion concerns the family of planar periodic dispersing billiards described above, whose quotient by stable manifolds yields a nonuniformly expanding map, together with th…