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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, symbolic dynamics is the practice of modelling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the shift operator.The idea goes back to Jacques Hadamard''s 1898 paper on the geodesics on surfaces of negative curvature. It was applied by Marston Morse in 1921 to the construction of a nonperiodic recurrent geodesic. Related work was done by Emil Artin in 1924 (for the system now called Artin billiard), P. J. Myrberg, Paul Koebe, Jakob Nielsen, G. A. Hedlund.