Geodesic
The dynamical Manin–Mumford problem for plane polynomial automorphisms
Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3421-3465.

Voir la notice de l'article provenant de la source EMS Press

Let f be a polynomial automorphism of the affine plane. In this paper we consider the possibility for it to possess infinitely many periodic points on an algebraic curve C. We conjecture that this happens if and only if f admits a time-reversal symmetry; in particular the Jacobian Jac (f) must be a root of unity.
DOI : 10.4171/jems/743
Classification : 37-XX, 32-XX
Keywords: Dynamical Manin–Mumford problem, polynomial automorphisms of the plane, dynamical heights, arithmetic equidistribution, non-Archimedean dynamics, non-uniform hyperbolicity 
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     title = {The dynamical {Manin{\textendash}Mumford} problem for plane polynomial automorphisms},
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Romain Dujardin; Charles Favre. The dynamical Manin–Mumford problem for plane polynomial automorphisms. Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3421-3465. doi : 10.4171/jems/743. http://geodesic.mathdoc.fr/articles/10.4171/jems/743/

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