Abstract
Let ~ be a finite set (called symbols) with the discrete topology and ~ = ~9~ be the set of all doubly infinite sequences of symbols with the product topology. We shall be interested in the homeomorphism ~:Zg~+ E~ which shifts a sequence one space to the left. In symbolic dynamics one studies a differentiable system (diffeomorphism or flow) by relating it to the shift homeomorphism ~. This idea started with Hadamard [ii] in 1898 when he set up a correspondence between geodesics on a surface of negative curvature with certain symbolic sequences. Then Marston Morse used this correspondence to construct a nonperiodic almost periodic geodesic [15], [16], [17]. Over the years Professor Hedlund has been active in symbolic dynamics (see for example [12] and [13]).
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