A flower theorem in $\mathbb{C}^n$

TL;DR

This paper extends the flower theorem to higher dimensions, proving an analogous result for specific complex germs that fix coordinate hyperspaces, broadening the understanding of complex dynamical systems.

Contribution

It introduces a higher-dimensional analog of the flower theorem for tangent to the identity germs fixing coordinate hyperspaces.

Findings

Proves an analog of the flower theorem in $\\mathbb{C}^n$

Applies to non-degenerate reduced tangent to the identity germs

Generalizes known results to arbitrary dimensions

Abstract

We prove an analog of the flower theorem for non-degenerate reduced tangent to the identity germs that fix the coordinate hyperspaces in any dimension.