How Many Real Attractive Fixed Points Can A Polynomial Have?

TL;DR

This paper establishes an upper bound on the number of attractive fixed points a complex polynomial can have on a line, specifically at most half its degree, and explores the problem in more general settings.

Contribution

It proves a new upper bound on the number of attractive fixed points of complex polynomials on a line and extends the analysis to more general cases.

Findings

A polynomial of degree n has at most ⌈n/2⌉ attractive fixed points on a line.

The paper extends the analysis to the general case beyond the line.

Provides bounds and conditions for attractive fixed points in complex polynomials.

Abstract

We prove a complex polynomial of degree $n$ has at most $\lceil n/2 \rceil$ attractive fixed points lying on a line. We also consider the general case.