Unlikely intersections problem for automorphisms of Markov surfaces
Algebraic Geometry
2025-04-24 v4 Dynamical Systems
Geometric Topology
Number Theory
Abstract
We study the problem of unlikely intersections for automorphisms of Markov surfaces of positive entropy. We show for certain parameters that two automorphisms with positive entropy share a Zariski dense set of periodic points if and only if they share a common iterate. Our proof uses arithmetic equidistribution for adelic line bundles over quasiprojective varieties, the theory of laminar currents and quasi-Fuchsian representation theory.
Cite
@article{arxiv.2401.05762,
title = {Unlikely intersections problem for automorphisms of Markov surfaces},
author = {Marc Abboud},
journal= {arXiv preprint arXiv:2401.05762},
year = {2025}
}