Joint partial equidistribution of Farey rays in negatively curved manifolds and trees

We prove a joint partial equidistribution result for common perpendiculars with given density on equidistributing equidistant hypersurfaces, towards a measure supported on truncated stable leaves. We recover a result of Marklof on the joint partial equidistribution of Farey fractions at a given dens...

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Published inErgodic theory and dynamical systems Vol. 44; no. 9; pp. 2700 - 2736
Main Authors PARKKONEN, JOUNI, PAULIN, FRÉDÉRIC
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.09.2024
Subjects
Density
Fractions
Hyperspaces
Lie groups
Trees
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Summary:We prove a joint partial equidistribution result for common perpendiculars with given density on equidistributing equidistant hypersurfaces, towards a measure supported on truncated stable leaves. We recover a result of Marklof on the joint partial equidistribution of Farey fractions at a given density, and give several analogous arithmetic applications, including in Bruhat–Tits trees.
Bibliography:ObjectType-Article-1
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ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2023.116