This classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work. The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century.

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."

How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle has produced an authoritative and elegant book--a model of clarity, succinctness, and with humor bordering on the sardonic. Ruelle is a professor of theoretical physics in France.

"Das Buch des Mathematikers und Physikers David Ruelle ist amusant und lehrreich. Amusant, weil es aus der seltsamen Welt der Mathematiker berichtet, und lehrreich, weil es die Grundideen schwieriger Theorien einfach darstellt... Ich habe das erfreulich kurze Buch mit grossem Vergnugen gelesen und empfehle es jedem, der Spass an spielerisch vorgetragenen genauen Uberlegungen hat..."
#"Prof. Dr. Henning Genz, Spektrum der Wissenschaft 7/93"#"

Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of sub -units. It is aimed at mathematicians interested in ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems, notably Anosov diffeomorphisms and flows. It is also of interest to theoretical physicists concerned with the conceptual basis of equilibrium statistical mechanics. The level of the presentation is generally advanced, the objective being to provide an efficient research tool and a text for use in graduate teaching. Background material on mathematics has been collected in appendices to help the reader. Extra material is given in the form of updates of problems that were open at the original time of writing and as a new preface specially written for this new edition by the author.