Fibonacci-like unimodal inverse limit spaces and the core Ingram conjecture

TL;DR

This paper investigates the structure of inverse limit spaces of Fibonacci-like tent maps, proving the Ingram Conjecture for their cores by analyzing symmetric arcs and their combinatorial properties.

Contribution

It introduces a detailed analysis of symmetric arcs in Fibonacci-like inverse limit spaces, leading to a proof of the Ingram Conjecture for these systems.

Findings

Link-symmetric arcs are symmetric or concatenations of quasi-symmetric arcs.

The structure of inverse limit spaces is clarified for Fibonacci-like tent maps.

The Ingram Conjecture is proven for the cores of Fibonacci-like unimodal inverse limits.

Abstract

We study the structure of inverse limit space of so-called Fibonacci-like tent maps. The combinatorial constraints implied by the Fibonacci-like assumption allow us to introduce certain chains that enable a more detailed analysis of symmetric arcs within this space than is possible in the general case. We show that link-symmetric arcs are always symmetric or a well-understood concatenation of quasi-symmetric arcs. This leads to the proof of the Ingram Conjecture for cores of Fibonacci-like unimodal inverse limits.