2009/06/22 by David Ralston, Ralston, David · 1 citation
Computer Science · Mathematics · #37B10 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #msc:37B10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0906.4003
14 Pages, to appear in Discrete and Continuous Dynamical Systems
arxiv created 2009/06/22 · openalex publication_date 2009/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Heaviness refers to a sequence of partial sums maintaining a certain lower bound and was recently introduced and studied in "Heaviness: and Extension of a Lemma of Y. Peres." After a review of basic properties to familiarize the reader with the ideas of heaviness, general principles of heaviness in symbolic dynamics are introduced. The classical Morse sequence is used to study a specific example of heaviness in a system with nontrivial rational eigenvalues. To contrast, Sturmian sequences are examined, including a new condition for a sequence to be Sturmian.