ISLES OF EDEN AND THE ZUK THEOREM IN ℝd
Barnabás M. Garay, Leon Ong Chua · International Journal of Bifurcation and Chaos · 2008
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.