Orbital counting for relatively Anosov groups

Richard Canary; Tengren Zhang; Feng Zhu; Andrew Zimmer

Orbital counting for relatively Anosov groups

Dynamical Systems 2026-07-28 v1 Differential Geometry Metric Geometry

Authors: Richard Canary , Tengren Zhang , Feng Zhu , Andrew Zimmer

Abstract

We obtain orbital counting results for relatively Anosov groups with respect to linear functionals with finite critical exponent. Our counting results follow from an equidistribution result and rely crucially on previous equidistribution results obtained in our proof of counting results for periods. Our results generalize earlier work of Sambarino in the setting of Anosov groups.

Cite

@article{arxiv.2607.25773,
  title  = {Orbital counting for relatively Anosov groups},
  author = {Richard Canary and Tengren Zhang and Feng Zhu and Andrew Zimmer},
  journal= {arXiv preprint arXiv:2607.25773},
  year   = {2026}
}

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19 pages