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A note on the shift on the Cantor set. (English) Zbl 0768.54028
Summary: Let \(O(x)\) be the orbit of \(x\) under a homeomorphism \(h\) on a metric space \(X\). It is shown that this motion can be found in the shift on the Cantor set; i.e. there is an embedding \(f: O(x)\to\{0,1\}^ Z\) such that \(\sigma\circ j=j\circ h\).

MSC:
54H20 Topological dynamics (MSC2010)
Keywords:
orbit; shift; Cantor set
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References:
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