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arXiv · 2401.05762

Unlikely intersections problem for automorphisms of Markov surfaces

Marc Abboud
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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.

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Marc Abboud. 2024-01-11. Unlikely intersections problem for automorphisms of Markov surfaces. https://arxiv.org/abs/2401.05762

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