Count lifts of non-maximal closed horocycles on $SL_N(\mathbb{Z}) \backslash SL_N(\mathbb{R})/SO_N({\mathbb{R}})$

DOI10.1007/S00605-022-01803-0arXiv2111.09584MaRDI QIDQ6383362

Publication date: 18 November 2021

Abstract: A closed horocycle

m a t h c a l U

on

has many lifts to the universal cover

S L_{N} (m a t h b b R) / S O_{N} (m a t h b b R)

. Under some conditions on the horocycle, we give a precise asymptotic count of its lifts of bounded distance away from a given base point in the universal cover. This partially generalizes previous work of Mohammadi--Golsefidy.

Mathematics Subject Classification ID

Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Homogeneous flows (37A17)

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