Non-expansion in polynomial automorphisms of $\mathbb{C}^2$

TL;DR

This paper investigates the behavior of polynomial automorphisms of complex two-dimensional space, focusing on the non-expansion properties within the context of the higher-dimensional Elekes-Szabó problem.

Contribution

It introduces new insights into the dynamics of Aut(C^2) actions, specifically addressing non-expansion phenomena in polynomial automorphisms.

Findings

Identification of conditions for non-expansion in polynomial automorphisms

Extension of the Elekes-Szabó problem to complex two-dimensional automorphisms

New techniques for analyzing automorphism actions on C^2

Abstract

We treat the higher-dimensional Elekes-Szab\'o problem in the case of the action of Aut(C^2) on C^2.