Dynamical invariants for group automorphisms

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.

References in corpus (4)

• Dirichlet series for finite combinatorial rank dynamics
• Orbit-counting for nilpotent group shifts
• A note on the dynamical zeta function of general toral endomorphisms
• Finite entropy characterizes topological rigidity

Cited by in corpus (10)

• Approximate lattices
• Towards a Polya-Carlson dichotomy for algebraic dynamics
• Single and multiple recurrence along non-polynomial sequences
• Dold sequences, periodic points, and dynamics
• A remark on $\mathbb{T}$-valued cohomology groups of algebraic group actions
• Directional uniformities, periodic points, and entropy
• Weak ergodic averages over dilated measures
• Optimal Diophantine Exponents for $\mathrm{SL}(n)$
• Khintchine-type double recurrence in abelian groups
• Simultaneous approximation in nilsystems and the multiplicative thickness of return-time sets