Asymptotic parameterization in inverse limit spaces of dendrites

TL;DR

This paper investigates the asymptotic behavior in inverse limit spaces of dendrites with a focus on symbolic dynamics and classification of asymptotic parameterizations to distinguish topological spaces.

Contribution

It introduces conditions for asymptotic parameterizations in inverse limit spaces of dendrites using symbolic dynamics, aiding topological classification.

Findings

Conditions for asymptotic parameterizations are established.

Asymptotic classification serves as a topological invariant.

The study enhances understanding of inverse limit spaces with periodic critical points.

Abstract

In this paper, we study asymptotic behavior arising in inverse limit spaces of dendrites. In particular, the inverse limit is constructed with a single unimodal bonding map, for which points have unique itineraries and the critical point is periodic. Using symbolic dynamics, sufficient conditions for two rays in the inverse limit space to have asymptotic parameterizations are given. Being a topological invariant, the classification of asymptotic parameterizations would be a useful tool when determining if two spaces are homeomorphic.