Chaos and the recurrent set (Q1766426)

The author examines the recurrent set \(R(f)\) of a continuous interval map \(f\). (1) If \(f\) has zero topological entropy, then \(R(f)\) is a \(G_{\delta}\) set. (2) \(R(f)\) is typically closed for continuous functions with zero topological entropy. (3) If the map sending \(x\) into its \(\omega\)-limit set \(\omega(x)\) is in the first Baire class, then \(R(f)\) is closed.