Orbits of automorphism groups of affine surfaces over $p$-adic fields

TL;DR

This paper investigates the behavior of automorphism groups acting on affine surfaces over $p$-adic fields, focusing on orbit closures and stationary measures to understand their dynamical properties.

Contribution

It provides new insights into the structure of automorphism groups of $p$-adic affine surfaces and their orbit dynamics, an area with limited prior exploration.

Findings

Characterization of orbit closures for automorphism groups

Identification of stationary measures on $p$-adic affine surfaces

New dynamical properties of automorphisms over $p$-adic fields

Abstract

We study orbit closures and stationary measures for groups of automorphisms of $p$-adic affine surfaces.