Non-Archimedean Hénon Maps
Hénon maps are among the most studied dynamical systems over the real and complex numbers, classical examples of polynomial automorphisms of the plane with rich, chaotic behavior. Arithmetic dynamics asks what happens when the same maps are iterated over very different number systems — non-Archimedean fields such as the p-adic numbers, where the notion of distance behaves in fundamentally different ways.
This paper studies the dynamics of Hénon maps in the non-Archimedean setting, analyzing the behavior of their orbits over these fields.