September 12, 2024Open Access

Intersection of orbits of loxodromic automorphisms of affine surfaces

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Abstract

We show the following result: If X₀ is an affine surface over a field K and f, g are two loxodromic automorphisms with an orbit meeting infinitely many times, then f and g must share a common iterate. The proof uses the preliminary work of the author in Abb23 on the dynamics of endomorphisms of affine surfaces and arguments from arithmetic dynamics. We then show a dynamical Mordell-Lang type result for surfaces in X₀ X₀.

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Cite This Study

Marc Abboud (Thu,) studied this question.

synapsesocial.com/papers/68e58ba1b6db64358752751b https://doi.org/https://doi.org/10.48550/arxiv.2409.07826

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