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Thermodynamic Formalism
  • Cited by 265
  • 2nd edition
  • David Ruelle, Institut des Hautes Études Scientifiques, France
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Book description

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 subunits. 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.

Reviews

‘This is the second edition of the already classical book on the theory of thermodynamic formalism by David Ruelle.‘

Source: Monatshefte für Mathematik

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Contents

References
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Oseledec, V. I., “A multiplicative ergodic theorem. Ljapunov characteristic numbers for dynamical systems,” Trudy Moscov. Mat. Obšč. 19, 179–210 (1968). English translation, Trans. Moscow Math. Soc.19, 197–231 (1968)
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W. Parry “Topological Markov chains and suspensions,” Warwick preprint, 1974
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Ratner, M., “Anosov flows with Gibbs measures are also Bernoullian,” Israel J. Math. 17, 380–391 (1974)
Robinson, R. M., “Undecidability and nonperiodicity for tilings of the plane,” Inventiones Math. 12, 177–209 (1971)
Robinson, D. W. and Ruelle, D., “Mean entropy of states in classical statistical mechanics.” Commun. Math. Phys. 5, 288–300 (1967)
Rohlin, V. A., “On the fundamental ideas of measure theory,” Mat. Sbornik (N. S.) 25, 107–150 (1949). English translation, Amer. Math. Soc. Transl., Ser. 1, 10, 1–54 (1952)
Ruelle, D., “A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule,” Commun. Math. Phys. 5, 324–329 (1967)
Ruelle, D., “Statistical mechanics of a one-dimensional lattice gas,” Commun. Math. Phys. 9, 267–278 (1968)
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Ruelle, D., “Statistical mechanics on a compact set with Zθ-action satisfying expansiveness and specification,” Bull. Amer. Math. Soc. 78, 988–991 (1972); Trans. Amer. Math. Soc. 185, 237–251 (1973)
Ruelle, D., “A measure associated with axiom A attractors,” Amer. J. Math. 98, 619–654 (1976)
Ruelle, D., “Generalized zeta-functions for axiom A basic sets,” Bull. Amer. Math. Soc. 82, 153–156 (1976)
Ruelle, D., “Zeta-functions for expanding maps and Anosov flows,” Inventiones Math. 34, 231–242 (1976)
Ruelle, D., “A heuristic theory of phase transitions,” Commun. Math. Phys., 53, 195–208 (1977)
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