A dichotomy in orbit-growth for commuting automorphisms
classification
🧮 math.DS
keywords
automorphismscommutingdichotomyorbitsperiodicactionsasymptoticasymptotically
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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.
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