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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Shrinking target problems for flows on homogeneous spaces


Authors: Dubi Kelmer and Shucheng Yu
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 37A17; Secondary 22E40
DOI: https://doi.org/10.1090/tran/7783
Published electronically: February 25, 2019
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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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Additional Information

Dubi Kelmer
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467-3806
Email: kelmer@bc.edu

Shucheng Yu
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467-3806
Email: shucheng.yu@bc.edu

DOI: https://doi.org/10.1090/tran/7783
Received by editor(s): February 14, 2018
Received by editor(s) in revised form: December 9, 2018
Published electronically: February 25, 2019
Additional Notes: This work was partially supported by NSF grant DMS-1401747 and NSF CAREER grant DMS-1651563.
Article copyright: © Copyright 2019 American Mathematical Society