The Core Ingram Conjecture for non-recurrent critical points

TL;DR

This paper proves the Core Ingram Conjecture for tent maps with non-recurrent, non-preperiodic critical points, establishing that their inverse limit spaces are non-homeomorphic when slopes differ.

Contribution

It provides a proof of the Core Ingram Conjecture for a new class of tent maps with specific critical point behavior, expanding understanding of inverse limit spaces.

Findings

Inverse limit spaces of such tent maps are non-homeomorphic with different slopes

The proof applies to maps with non-recurrent, non-preperiodic critical points

Supports the conjecture in a broader class of dynamical systems

Abstract

We study inverse limit spaces of tent maps, and the Ingram Conjecture, which states that the inverse limit spaces of tent maps with different slopes are non-homeomorphic. When the tent map is restricted to its core, so there is no ray compactifying on the inverse limit space, this result is referred to as the Core Ingram Conjecture. We prove the Core Ingram Conjecture when the critical point is non-recurrent and not preperiodic.