Quantitative behavior of unipotent flows and an effective avoidance principle

Elon Lindenstrauss*, Gregorii Margulis, Amir Mohammadi, Nimish A. Shah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We give an effective bound on how much time orbits of a unipotent group U on an arithmetic quotient G/Γ can stay near homogeneous subvarieties of G/Γ corresponding to ℚ-subgroups of G. In particular, we show that if such a U-orbit is moderately near a proper homogeneous subvariety of G/Γ for a long time, it is very near a different homogeneous subvariety. Our work builds upon the linearization method of Dani and Margulis. Our motivation in developing these bounds is in order to prove quantitative density statements about unipotent orbits, which we plan to pursue in a subsequent paper. New qualitative implications of our effective bounds are also given.

Original languageAmerican English
JournalJournal d'Analyse Mathematique
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Hebrew University of Jerusalem.


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