We present some recurrence results in the context of ergodic theory and dynamical systems.
The main focus will be on smooth dynamical systems, in particular, those with some …

In this paper we prove that the Poincaré map associated to a Lorenz-like flow has
exponential decay of correlations with respect to Lipschitz observables. This implies that the …

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 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 study the distribution of hitting times for a class of random dynamical
systems. We prove that for invariant measures with super-polynomial decay of correlations …

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 …

We consider the recurrence time to the r-neighbourhood for interval exchange maps. For
almost every interval exchange map we show that the logarithm of the recurrence time …

This paper proves shrinking target results for IETs. Let {a_1\geq a_2\geq...} be a sequence
of positive real numbers with divergent sum. Then for almost every IET T, the limsup of B (T …

The dominating methodology used in the study of dynamical systems is the geometric
picture introduced by Poincaré. The focus is on the structure of the state space and the …