A flower theorem in dimension two

TL;DR

This paper establishes a two-dimensional version of the Leau-Fatou flower theorem, extending classical results on local dynamics near fixed points for certain biholomorphic maps.

Contribution

It introduces a novel two-dimensional analog of the Leau-Fatou flower theorem for non-degenerate tangent to the identity biholomorphisms.

Findings

Proves a two-dimensional Leau-Fatou flower theorem

Extends classical one-dimensional dynamics results

Provides new insights into biholomorphic fixed point behavior

Abstract

We prove a two-dimensional analog of Leau-Fatou flower theorem for non-degenerate reduced tangent to the identity biholomorphisms.