Abstract For any β> 1, let (0, 1, T β) be the beta dynamical system. For a positive function ψ:
ℕ→ ℝ+ and a real number x 0∈ 0, 1, we define D\left (T_ β, ψ, x_0\right) the set of ψ-well …

We prove that if a system has superpolynomial (faster than any power law) decay of
correlations then the time $\tau_ {r}(x, x_ {0}) $ needed for a typical point $ x $ to enter for the …

We investigate the connection between the dynamical Borel-Cantelli and waiting time
results. We prove that if a system has the dynamical Borel-Cantelli property, then the time …

We study in this paper estimates on the size of the sets of points which are well
approximated by orbits of other points under certain dynamical systems. We apply the …

A classical Borel Cantelli Lemma gives conditions for deciding whether an infinite number of
rare events will almost surely happen. In this article, we propose an extension of Borel …

We consider toral extensions of hyperbolic dynamical systems. We prove that its quantitative
recurrence (also with respect to given observables) and hitting time scale behavior depend …

In this paper, we investigate a modified version of the shrinking target problem on self-
conformal sets, which unifies the shrinking target problems and quantitative recurrence …

Let $\tau_r (x, x_0) $ be the time needed for a point $ x $ to enter for the first time in a ball $
B_r (x_0) $ centered in $ x_0 $, with small radius $ r $. We construct a class of translations …

In this note we prove that for equilibrium states of axiom A systems having positive
dimension the time τ B (x) needed for a typical point x to enter for the first time in a typical …

Three properties of dynamical systems (recurrence, connectivity and proximality) are
quantified by introducing and studying the gauges (measurable functions) corresponding to …