A Combinatorial Characterization of the Critical Itineraries of a Uniform Dynamical System

2012/05/26 by Michael F. Barnsley, Barnsley, Michael, Wolfgang Steiner +3
Mathematics · Physics and Astronomy · #05 #37 #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1205.5902

openalex publication_date 2012/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.

Citations

• Deterministic Nonperiodic Flow

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