zbMATH — the first resource for mathematics

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 \(\sigma\circ j=j\circ h\).

54H20 Topological dynamics (MSC2010)
orbit; shift; Cantor set
Full Text: DOI
[1] J. M. Aarts, The structure of orbits in dynamical systems, Fund. Math. 129 (1988), no. 1, 39 – 58. · Zbl 0664.54026
[2] R. D. Anderson, On raising flows and mappings, Bull. Amer. Math. Soc. 69 (1963), 259 – 264. · Zbl 0113.38104
[3] H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton University Press, Princeton, N.J., 1981. M. B. Porter Lectures. · Zbl 0459.28023
[4] Marston Morse and Gustav A. Hedlund, Symbolic Dynamics, Amer. J. Math. 60 (1938), no. 4, 815 – 866. · Zbl 0019.33502
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.