Lacunary series, resonances, and automorphisms of $\mathbb{C}^2$ with a round Siegel domain

TL;DR

This paper constructs transcendental automorphisms of complex two-dimensional space with unbounded, regular Siegel domains, advancing understanding of complex dynamics and automorphism groups.

Contribution

It introduces new transcendental automorphisms of ^2 with specific geometric properties, particularly unbounded regular Siegel domains.

Findings

Constructed transcendental automorphisms with unbounded Siegel domains

Demonstrated existence of automorphisms with specific dynamical features

Enhanced understanding of automorphisms in complex two-dimensional spaces

Abstract

We construct transcendental automorphims of $\mathbb{C}^{2}$ having an unbounded and regular Siegel domain.