Symbolic dynamics and transformations of the unit interval

Parry, William

doi:10.1090/S0002-9947-1966-0197683-5

Symbolic dynamics and transformations of the unit interval

Author: William Parry
Journal: Trans. Amer. Math. Soc. 122 (1966), 368-378
MSC: Primary 28.75
DOI: https://doi.org/10.1090/S0002-9947-1966-0197683-5
MathSciNet review: 0197683
Full-text PDF Free Access

References | Similar Articles | Additional Information

William Parry, Intrinsic Markov chains, Trans. Amer. Math. Soc. 112 (1964), 55–66. MR 161372, DOI https://doi.org/10.1090/S0002-9947-1964-0161372-1
E. R. Van Kampen, The Topological Transformations of a Simple Closed Curve Into Itself, Amer. J. Math. 57 (1935), no. 1, 142–152. MR 1507062, DOI https://doi.org/10.2307/2372026
S. M. Ulam, Problems in modern mathematics, Science Editions John Wiley & Sons, Inc., New York, 1964. MR 0280310
P. R. Stein and S. M. Ulam, Non-linear transformation studies on electronic computers, Rozprawy Mat. 39 (1964), 66. MR 169416
A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar. 8 (1957), 477–493. MR 97374, DOI https://doi.org/10.1007/BF02020331
Walter Helbig Gottschalk and Gustav Arnold Hedlund, Topological dynamics, American Mathematical Society Colloquium Publications, Vol. 36, American Mathematical Society, Providence, R. I., 1955. MR 0074810
R. L. Adler, A. G. Konheim, and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309–319. MR 175106, DOI https://doi.org/10.1090/S0002-9947-1965-0175106-9
Konrad Jacobs, Ergodic decomposition of the Kolmogoroff-Sinai invariant, Ergodic Theory (Proc. Internat. Sympos., Tulane Univ., New Orleans, La., 1961) Academic Press, New York, 1963, pp. 173–190. MR 0197677
A. I. Khinchin, Mathematical foundations of information theory, Dover Publications, Inc., New York, N. Y., 1957. Translated by R. A. Silverman and M. D. Friedman. MR 0092709
Leo Breiman, On achieving channel capacity in finite-memory channels, Illinois J. Math. 4 (1960), 246–252. MR 118574
A. O. Gel′fond, A common property of number systems, Izv. Akad. Nauk SSSR. Ser. Mat. 23 (1959), 809–814 (Russian). MR 0109817
W. Parry, On the $\beta $-expansions of real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960), 401–416 (English, with Russian summary). MR 142719, DOI https://doi.org/10.1007/BF02020954