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math.AG2024
Intersection of orbits of loxodromic automorphisms of affine surfaces
Marc Abboud
We show the following result: If is an affine surface over a field and are two loxodromic automorphisms with an orbit meeting infinitely many times, then and $…
math.AG2024
Rigidity of periodic points for loxodromic automorphisms of affine surfaces
Marc Abboud
We show that two automorphisms of an affine surface with dynamical degree strictly larger than 1 share a Zariski dense set of periodic points if and only if they have the same peri…
math.AG2024
Unlikely intersections problem for automorphisms of Markov surfaces
Marc Abboud
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…