Another construction of a Cantor bouquet at a fixed indeterminate point

Abstract

In this article, we study the local dynamical structure of a rational mapping $F$ of ${\mathbf{P}}^2$ at a fixed indeterminate point $p$. Using a sequence of blowups, we construct a family $\{{\tilde{W}}_{\mathbf{j}}{\}}_{\mathbf{j}\in J}$ of germs of holomorphic curve at the point $p$, where $J$ is a subset of a Cantor set $\{1,2{\}}^{\mathbf{N}}$. This is a new construction for a Cantor bouquet.