Let (Bi) be a sequence of measurable sets in a probability space (X,B, Î¼) such that âˆ‘âˆžn=1 Î¼(Bi) = âˆž. The classical Borelâ€“Cantelli lemma states that if the sets Bi are independent, then Î¼({x âˆˆ X : x âˆˆâ€¦ (More)

We obtain geometric upper bounds on the topological entropy of generalized polygon exchange transformations. As an application of our results, we show that billiards in polygons and rational polytopsâ€¦ (More)

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return timesâ€¦ (More)

We prove that the transfer operator for a general class of rational maps converges exponentially fast in the supremum norm and in HH older norms for small enough HH older exponents to its principalâ€¦ (More)

Given an ergodic dynamical system (X, T, Âµ), and U âŠ‚ X measurable with Âµ(U) > 0, let Âµ(U)Ï„ U (x) denote the normalized hitting time of x âˆˆ X to U. We prove that given a sequence (U n) with Âµ(U n) â†’â€¦ (More)

We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples includeâ€¦ (More)

The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almostâ€¦ (More)

Suppose Bi := B(p, ri) are nested balls of radius ri about a point p in a dynamical system (T,X, Î¼). The question of whether T ix âˆˆ Bi infinitely often (i.o.) for Î¼ a.e. x is often called theâ€¦ (More)