ISLES OF EDEN AND THE ZUK THEOREM IN ℝ^d

The concept of isles of Eden when generalized from finite cellular automata to classical dynamical systems on ℝ d calls the attention to the ZUK Theorem — Z for [Zubov, 1957], U and K for [Ura & Kimura, 1960] — a fifty years old and almost forgotten result in topological dynamics, a classification theorem for compact isolated invariant sets. We provide a simple proof and discuss various consequences including a new result on pointwise Liapunov functions.