Miles, Richard; Staines, Matthew; Ward, Thomas Dynamical invariants for group automorphisms. (English) Zbl 1332.37021 Bhattacharya, Siddhartha (ed.) et al., Recent trends in ergodic theory and dynamical systems. International conference in honor of S. G. Dani’s 65th birthday, Vadodara, India, December 26–29, 2012. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-0931-9/pbk; 978-1-4704-2219-6/ebook). Contemporary Mathematics 631, 231-258 (2015). Summary: 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.For the entire collection see [Zbl 1309.37003]. Cited in 4 Documents MSC: 37C35 Orbit growth in dynamical systems 37B40 Topological entropy 57S10 Compact groups of homeomorphisms 20E36 Automorphisms of infinite groups Keywords:topological entropy; zeta function; group automorphism; Mertens theorem; one-solenoid; Lehmer’s problem; orbit Dirichlet series; Bernoulli shift; Ornstein theory PDFBibTeX XMLCite \textit{R. Miles} et al., Contemp. Math. 631, 231--258 (2015; Zbl 1332.37021)