2019/03/18 by Chris Good, Good, Chris, Robin Knight +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS
paper · pdf · doi:10.48550/arxiv.1903.07529
arxiv created 2019/03/18 · openalex publication_date 2019/03/18 · arxiv updated 2019/03/19 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let f be a unimodal map of the interval with critical point c. If the orbit of c is not dense then most points in lim[0,1],f have neighborhoods that are homeomorphic with the product of a Cantor set and an open arc. The points without this property are called inhomogeneities, and the set, I, of inhomogeneities is equal to lim ω(c),f| ω(c) . In this paper we consider the relationship between the limit complexity of ω(c) and the limit complexity of I. We show that if ω(c) is more complicated than a finite collection of convergent sequences then I can have arbitrarily high limit complexity. We give a complete description of the limit complexity of I for any possible ω(c).