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Bibliography
R. L. Adler, A. G. Konheim andM. H. McAndrew, Topological entropy,Trans. Amer. Math. Soc. 114 (1965), 309–319.
Kiyoshi Aoki, On symbolic representation,Proc. Japan Acad. 30 (1954), 160–164.
Emil Artin, Ein mechanisches System mit quasiergodischen Bahnen,Abh. Math. Sem. Univ. Hamburg 3 (1924), 170–175.
G. D. Birkhoff,Dynamical Systems, Amer. Math. Soc. Colloq. Publ., Vol. 9, American Mathematical Society, Providence; first edition, 1927; revised edition, 1966.
G. D. Birkhoff, Sur le problème restreint des trois corps (Second mémoire),Ann. Scuola Nor. Sup. Pisa 5 (1936), 9–50.
J. D. Ferguson,Some Properties of Mappings on Sequence Spaces, Dissertation, Yale University, 1962.
Harry Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation,Math. Systems Theory 1 (1967), 1–49.
W. H. Gottschalk, Substitution minimal sets,Trans. Amer. Math. Soc. 109 (1963), 467–491.
W. H. Gottschalk, Minimal sets: An introduction to topological dynamics,Bull. Amer. Math. Soc. 64 (1958), 336–351.
W. H. Gottschalk andG. A. Hedlund,Topological Dynamics, Amer. Math. Soc. Colloq. Publ., Vol. 36, American Mathematical Society, Providence, 1955.
W. H. Gottschalk andG. A. Hedlund, A characterization of the Morse minimal set,Proc. Amer. Math. Soc. 15 (1964), 70–74.
Frank Hahn andYitzhak Katznelson, On the entropy of uniquely ergodic transformations.Trans. Amer. Math. Soc. 126 (1967), 335–360.
Paul R. Halmos,Lectures on Ergodic Theory, Publ. Math. Soc. Japan, No. 3, Tokyo, 1956.
Paul R. Halmos,Entropy in Ergodic Theory, Univ. of Chicago Press, Chicago, 1959.
G. A. Hedlund, Sturmian minimal sets,Amer. J. Math. 66 (1944), 605–620.
G. A. Hedlund, Mappings on sequence spaces (Part I), Comm. Research Div. Technical Report No. 1, Princeton, N. J., Feb. 1961.
G. A. Hedlund, Transformations commuting with the shift,Topological Dynamics (An International Symposium), Joseph Auslander and Walter H. Gottschalk (Editors), W. A. Benjamin, New York, 1968.
S. Kakutani, Ergodic Theory of Shift Transformations,Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability Theory II (1967), pp. 405–414.
E. A. Michael, Continuous selections II,Ann. of Math. 64 (1956), 562–580.
Marston Morse, Recurrent geodesics on a surface of negative curvature,Trans. Amer. Math. Soc. 22 (1921), 84–100.
Marston Morse,Symbolic Dynamics, Lectures by Marston Morse 1937–1938, Notes by Rufus Oldenburger, The Institute for Advanced Study, Princeton, N. J., 1966.
Marston Morse andG. A. Hedlund, Symbolic dynamics,Amer. J. Math. 60 (1938), 815–866.
Marston Morse andG. A. Hedlund, Symbolic dynamics II. Sturmian trajectories,Amer. J. Math. 62 (1940), 1–42.
J. C. Oxtoby, Ergodic sets,Bull. Amer. Math. Soc. 58 (1952), 116–136.
William Parry, Symbolic dynamics and transformations of the unit interval,Trans. Amer. Math. Soc. 122 (1966), 368–378.
William Reddy, Lifting expansive homeomorphisms to symbolic flows,Math. Systems Theory 2 (1968), 91–92.
Stephen Smale, Diffeomorphisms with many periodic points,Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), edited by S. S. Cairns, Princeton University Press, Princeton, 1965, pp. 63–80.
W. R. Utz, Almost periodic geodesics on manifolds of hyperbolic type,Duke Math. J. 18 (1951), 147–164.
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This research was partially supported by the Army Research Office (Durham).
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Hedlund, G.A. Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3, 320–375 (1969). https://doi.org/10.1007/BF01691062
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DOI: https://doi.org/10.1007/BF01691062