A dichotomy in orbit-growth for commuting automorphisms
arXiv:0904.3492 · doi:10.1112/jlms/jdq010
Abstract
We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts, and those for which there is no excess of periodic orbits.