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These notes survey the results about Axiom A diffeomorphisms obtained since Smale's well-known paper of 1967. In that paper, Smale defined these diffeomorphisms and set up a program for dynamical systems centered around them. These examples are charming in that they display complicated behavior but are still intelligible. This means that there are many theorems and yet some open problems. The first two sections copy Smale's paper for completeness. The last sections deal with certain non Axiom A systems that have received a good deal of attention. These systems display a certain amount of Axiom A type of behavior. ... Read more

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This early works is a fascinating collection of easy to follow recipes with much of the information still useful and practical today. Many of the earliest books, particularly those dating back to the 1900's and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork. ... Read more

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For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details.

From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."