Shrinking target problems for flows on homogeneous spaces

Kelmer, Dubi; Yu, Shucheng

doi:10.1090/tran/7783

Shrinking target problems for flows on homogeneous spaces
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by Dubi Kelmer and Shucheng Yu PDF

Trans. Amer. Math. Soc. 372 (2019), 6283-6314 Request permission

Abstract:

We study shrinking targets problems for discrete time flows on a homogeneous space $\Gamma \backslash G$ 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 by Athreya and Margulis.

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