Dynamical borel-cantelli lemma for hyperbolic spaces

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Distribution of full cylinders and the Diophantine properties of the orbits in $\beta$-expansions (2014, background): “For the background and more results on shrinking target problems, the reader is referred to [1], [2], [3], [4], [8], [9], [10], [11], [12], [20], [21], [24], and [25] and the references quoted therein.”
Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence (2009, background): “acing balls with other suitable target sets) have been proved in many continuous time dynamical systems of geometrical interest: geodesic ﬂows, unipotent ﬂows, homogeneous spaces, etc. etc. (see e.g. [6, 20, 23, 38, 30, 32]). For discrete time systems this kind of results hold in general if the syst”
Logarithm laws for unipotent flows, I (2008, background): “hat A satisﬁes the STP for the sequence {gn}∞ n=0 if for any sequence {An}n∈N ⊂ A µ({x∈ X: gnx∈ An inﬁnitely often}) = ˆ 1 P∞ n=0 µ(An) = ∞ 0 otherwise There are many results on STP’s for hyperbolic ([4, 5, 8, 11]) and elliptic ([6, 16]) systems, but it would be interesting to obtain more results fo”