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Limiting distributions of translates of divergent diagonal orbits
Part of
Uri Shapira, Cheng Zheng
Journal:

Compositio Mathematica / Volume 155 / Issue 9 / September 2019

Published online by Cambridge University Press:

02 August 2019, pp. 1747-1793

Print publication:

September 2019
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We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite-volume orbits equidistribute in the ambient space. As an application of our results we prove an asymptotic formula for the number of integral points in a ball on some varieties as the radius goes to infinity.

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Limiting distributions of translates of divergent diagonal orbits