Shrinking target problems for flows on homogeneous spaces
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- by Dubi Kelmer and Shucheng Yu PDF
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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.References
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Additional Information
- Dubi Kelmer
- Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467-3806
- MR Author ID: 772506
- ORCID: 0000-0002-4182-7958
- Email: kelmer@bc.edu
- Shucheng Yu
- Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467-3806
- MR Author ID: 1234039
- Email: shucheng.yu@bc.edu
- 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.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 6283-6314
- MSC (2010): Primary 37A17; Secondary 22E40
- DOI: https://doi.org/10.1090/tran/7783
- MathSciNet review: 4024522