A poincaré section for the horocycle flow on the space of lattices

Jayadev S. Athreya, Yitwah Cheung

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a Poincaré section for the horocycle flow on the modular surface, and study the associated first return map, which coincides with a transformation [the Boca-Cobeli-Zaharescu (BCZ) map] defined by Boca et al. [7]. We classify ergodic invariant measures for this map and prove equidistribution of periodic orbits. As corollaries, we obtain results on the average depth of cusp excursions and on the distribution of gaps for Farey sequences and slopes of lattice vectors.

Original languageEnglish (US)
Pages (from-to)2643-2690
Number of pages48
JournalInternational Mathematics Research Notices
Volume2014
Issue number10
DOIs
StatePublished - 2014

ASJC Scopus subject areas

  • Mathematics(all)

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