Equidistribution and counting of periodic tori in the space of Weyl chambers

Nguyen-Thi Dang; Jialun Li

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arXiv · 2305.17070

Equidistribution and counting of periodic tori in the space of Weyl chambers

Nguyen-Thi Dang·Jialun Li

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Abstract

Let G be a semisimple Lie group without compact factor and $\Gamma$ < G a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber flows live on tori. We prove that these periodic tori equidistribute exponentially fast towards the quotient of the Haar measure. From the equidistribution formula, we deduce a higher rank prime geodesic theorem.

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Nguyen-Thi Dang, Jialun Li. 2023-05-26. Equidistribution and counting of periodic tori in the space of Weyl chambers. https://arxiv.org/abs/2305.17070

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