The shrinking target property of irrational rotations Page 1 Nonlinearity The shrinking target
property of irrational rotations To cite this article: Dong Han Kim 2007 Nonlinearity 20 1637 View …

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 …

Quantitative recurrence indicators are defined by measuring the first entrance time of the
orbit of a point $ x $ in a decreasing sequence of neighborhoods of another point $ y $. It is …

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 …

We consider the Rényi entropy function for weakly ψ-mixing systems. The first main result of
the paper establishes existence and regularity properties. The second main result is …

Over a-mixing dynamical system we consider the function (Cn)/n in the limit of large n, where
(Cn) is the first return of a cylinder of length n to itself. Saussol et al.([30]) proved that this …

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 …

Dynamical Diophantine approximation studies the quantitative properties of the distribution
of the orbits in a dynamical system. More precisely, it focuses on the size of dynamically …