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Shrinking target problems for flows on homogeneous spaces.(English)Zbl 1426.37006

Summary: We study shrinking targets problems for discrete time flows on a homogeneous space \(\Gamma \setminus G\) with \(G\) a semisimple group and \(\Gamma\) an irreducible lattice. Our results apply to both diagonalizable and unipotent flows and apply to very general families of shrinking targets. As a special case, we establish logarithm laws for cusp excursions of unipotent flows, settling a problem raised byJ. S. Athreya andG. A. Margulis [J. Mod. Dyn. 3, No. 3, 359–378 (2009;Zbl 1184.37007); J. Mod. Dyn. 11, 1–16 (2017;Zbl 1402.37003)].

MSC:

37A17 Homogeneous flows
22E40 Discrete subgroups of Lie groups
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)

Cite

References:

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[2]Athreya, Jayadev S.; Margulis, Gregory A., Logarithm laws for unipotent flows, II, J. Mod. Dyn., 11, 1-16 (2017) ·Zbl 1402.37003 ·doi:10.3934/jmd.2017001
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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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