On the genesis of symbolic dynamics as we know it

Volume 110 / 2008

Ethan M. Coven, Zbigniew H. Nitecki Colloquium Mathematicum 110 (2008), 227-242 MSC: Primary 37B10; Secondary 01A60. DOI: 10.4064/cm110-2-1


We trace the beginning of symbolic dynamics—the study of the shift dynamical system—as it arose from the use of coding to study recurrence and transitivity of geodesics. It is our assertion that neither Hadamard's 1898 paper, nor the Morse-Hedlund papers of 1938 and 1940, which are normally cited as the first instances of symbolic dynamics, truly present the abstract point of view associated with the subject today. Based in part on the evidence of a 1941 letter from Hedlund to Morse, we place the beginning of symbolic dynamics in a paper published by Hedlund in 1944.


  • Ethan M. CovenDepartment of Mathematics
    Wesleyan University
    Middletown, CT 06459, U.S.A.
  • Zbigniew H. NiteckiDepartment of Mathematics
    Tufts University
    Medford, MA 02155, U.S.A.

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