On a set of numbers arising in the dynamics of unimodal maps

TL;DR

This paper explores the arithmetical properties of a special set of numbers that encode the dynamics of unimodal maps, focusing on the Feigenbaum bifurcation and its associated topological zeta function.

Contribution

It introduces a new study of the arithmetical properties of numbers linked to unimodal map dynamics and the Feigenbaum bifurcation, connecting them with topological zeta functions.

Findings

Characterization of the arithmetical properties of the set of numbers

Analysis of the relationship between these numbers and the Feigenbaum bifurcation

Insights into the encoding of unimodal map dynamics

Abstract

In this paper we initiate the study of the arithmetical properties of a set numbers which encode the dynamics of unimodal maps in a universal way along with that of the corresponding topological zeta function. Here we are concerned in particular with the Feigenbaum bifurcation.