2022/09/07 by Fumio Hazama, Hazama, Fumio
Mathematics · Physics and Astronomy · #05E18 #37P25 #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2209.02868
openalex publication_date 2022/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present article introduces the notion of quasi-smoothness of marked rhythms through a certain transformation Ref, called reformation map. A marked rhythm consists of a rhythm together with a marker, and the map Ref modifies the marked onset of the rhythm. It is shown that an iteration of the map Ref transforms an arbitrary marked rhythm into a quasi-smooth one. A numerical criterion for a marked rhythm to be quasi-smooth is given in terms of the difference of its rhythm part. Through this criterion, the rhythm part of any quasi-smooth marked rhythm is shown to be smooth.