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Bowen was awarded a degree by the University of California at Berkeley and obtained a doctorate there in 1970. The same year he was appointed to Berkeley becoming a full professor there in 1977.
Dynamical systems theory had been started by Poincaré in the 1880's. Bowen's doctoral thesis, supervised by Stephen Smale, was on this topic and he continued to make major contributions to dynamical system theory, building on the work of Poincaré and Gibbs.
Bowen extended Gibbs' work on invariant measures associated with dynamical systems. He developed methods in symbolic dynamics originally due to Hadamard and Morse.
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