ISLES OF EDEN AND THE ZUK THEOREM IN ℝd

Abstract

The concept of isles of Eden when generalized from finite cellular automata to classical dynamical systems on ℝdcalls 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.