Asymptotic parameterization in inverse limit spaces of dendrites

2012/06/13 by Brent Hamilton, Hamilton, Brent
Materials Science · Mathematics · #37B10 #54F15 #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #math.DS #msc:37B10 #msc:54F15

paper · pdf · doi:10.48550/arxiv.1206.2780

arxiv created 2012/06/13 · openalex publication_date 2012/06/13 · arxiv updated 2012/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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