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ISLES OF EDEN AND THE ZUK THEOREM IN ℝ^d

BARNABAS M. GARAY

Department of Mathematics, Budapest University of Technology, H-1521 Budapest, Hungary

Computer and Automation, Institute (SZTAKI), Hungarian Academy of Sciences, H-1111 Budapest, Hungary

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and

LEON O. CHUA

Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA

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https://doi.org/10.1142/S0218127408022184Cited by:2 (Source: Crossref)

Abstract

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.

Keywords:

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