Let (Bi) be a sequence of measurable sets in a probability space (X, ℬ, μ) such that∑∞ n=
1μ (Bi)=∞. The classical Borel–Cantelli lemma states that if the sets Bi are independent …

We consider some non-uniformly hyperbolic invertible dynamical systems which are
modeled by a Gibbs–Markov–Young tower. We assume a polynomial tail for the inducing …

We consider finitely generated free semigroup actions on a compact metric space and
obtain quantitative information on Poincaré recurrence, average first return time and hitting …

We consider the 2D skew product $ F:(x, u)\mapsto (f (x), u+\tau (x)) $, where the base map $
f $ is a piecewise $\mathscr {C}^{2} $, covering and uniformly expanding the map of the …

We consider a general relation between fixed point stability of suitably perturbed transfer
operators and convergence to equilibrium (a notion which is strictly related to decay of …

Consider a mixing dynamical systems $([0, 1], T,\mu) $, for instance a piecewise expanding
interval map with a Gibbs measure $\mu $. Given a non-summable sequence $(m_k) $ of …

Given a dynamical system, we prove that the shortest distance between two n-orbits scales
like n to a power even when the system has slow mixing properties, thus building and …

In this paper we study the distributions of hitting and return times for observations of
dynamical systems. We apply the results to get an exponential law for the distributions of …

Suppose B i:= B (p, ri) are nested balls of radius ri about a point p in a dynamical system (T,
X, μ). The question of whether T ix∈ B i infinitely often (io) for μ ae x is often called the …

We consider a ϕ-mixing shift T on a sequence space Ω and study the number of returns {T k
ω∈ U} to a union U of cylinders of length n until the first return {T k ω∈ V} to another union V …