Recent Trends in Ergodic Theory and Dynamical Systems

2013/06/25 by Bhattacharya, Siddhartha, Richard Miles, Matthew Staines +4 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Abelian group #Advanced Differential Equations and Dynamical Systems #Algebra over a field #Automorphism #Automorphisms of the symmetric and alternating groups #Conjugacy class #Dynamical systems theory #Engineering #Ergodic theory #Geometry #Mathematical Dynamics and Fractals #Mathematics #Physics #Point (geometry) #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Range (aeronautics) #Theoretical physics #Topological conjugacy #math.DS #msc:11J72 #msc:37C35 #msc:37P35

paper · pdf · doi:10.1090/conm/631

published as Contemp. Mathematics, 631, 231-258 (2015)

arxiv created 2013/06/25 · openalex publication_date 2015/01/26 · arxiv updated 2016/10/27 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/05

Abstract

We discuss some of the issues that arise in attempts to classify automorphisms of compact abelian groups from a dynamical point of view. In the particular case of automorphisms of one-dimensional solenoids, a complete description is given and the problem of determining the range of certain invariants of topological conjugacy is discussed. Several new results and old and new open problems are described

Citations

• A note on the dynamical zeta function of general toral endomorphisms
• Mahler measure and entropy for commuting automorphisms of compact groups
• The structure of skew products with ergodic group automorphisms
• Abelian groups without elements of finite order
• Speculations Concerning the Range of Mahler's Measure
• Automorphisms of compact groups
• Differentiable dynamical systems

Cited by

• Directional uniformities, periodic points, and entropy
• Approximate lattices