No entire function with real multipliers in class S

TL;DR

This paper proves that no entire transcendental function within class S can have all repelling periodic orbits with real multipliers, highlighting a restriction on the dynamical behavior of such functions.

Contribution

It establishes a new impossibility result for entire transcendental functions in class S regarding the nature of their repelling periodic orbits.

Findings

No entire transcendental function in class S has all repelling periodic orbits with real multipliers.

The result constrains the dynamical properties of functions in class S.

This contributes to the understanding of the structure of Julia sets for such functions.

Abstract

We prove that there is no entire transcendental function in class S with real multipliers of all repelling periodic orbits.