# Attracting sequences of holomorphic automorphisms that agree to a certain order

## TL;DR

This paper proves that the basin of attraction for a sequence of holomorphic automorphisms, which agree to a certain order at a fixed point, is biholomorphic to complex n-space, with estimates on the necessary order.

## Contribution

It establishes conditions under which the basin of attraction is biholomorphic to ^n, including explicit estimates on the order of agreement needed.

## Key findings

- Basin of attraction is biholomorphic to ^n under certain conditions
- Provides explicit estimates for the order of agreement
- Extends understanding of dynamics of holomorphic automorphisms

## Abstract

The basin of attraction of a uniformly attracting sequence of holomorphic automorphisms that agree to a certain order in the common fixed point, is biholomorphic to $\mathbb{C}^n$. We also give sufficient estimates how large this order has to be.