An autocorrelation and discrete spectrum for dynamical systems on metric\n spaces

2016/08/19 by Daniel Lenz, Lenz, Daniel
Materials Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1608.05636

openalex publication_date 2016/08/19 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study dynamical systems (X,G,m) with a compact metric space X and a\nlocally compact, \σ-compact, abelian group G. We show that such a\nsystem has discrete spectrum if and only if a certain space average over the\nmetric is a Bohr almost periodic function. In this way, this average over the\nmetric plays for general dynamical systems a similar role as the\nautocorrelation measure plays in the study of aperiodic order for special\ndynamical systems based on point sets.\n

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