Thermodynamic formalism : the mathematical structures of equilibrium statistical mechanics
著者
書誌事項
Thermodynamic formalism : the mathematical structures of equilibrium statistical mechanics
（Cambridge mathematical library）
Cambridge University Press, 2004
2nd ed
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注記
Bibliography: p. 167-171
Includes index
内容説明・目次
内容説明
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.
目次
- 1. Introduction to the 2nd edition
- 2. Introduction
- 3. Theory of Gibbs States
- 4. Gibbs States: complements
- 5. Translation invariance: theory of equilibrium states
- 6. Connection between Gibbs States and equilibrium
- 7. One-dimensional systems
- 8. Extension of the thermodynamic formalism
- Appendix A.1. Miscellaneous definitions and results
- Appendix A.2. Topological dynamics
- Appendix A.3. Convexity
- Appendix A.4. Measures and abstract dynamical systems
- Appendix A.5. Integral representations on convex compact sets
- Appendix B. Open problems
- Appendix C. Flows
- Appendix D. Update of open problems.
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