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Complexity: Hierarchical Structures and Scaling in Physicsby Remo Badii
Synopses & ReviewsPublisher Comments:Very successful book in the Cambridge Nonlinear Science Series, now available in paperback. Review:"The approach throughout is no-nonsense...for a mathematically mature reader determined to ponder what complexity might mean, this book will provide some rewarding exercise." Nature"The book presents a comprehensive review of the results which have been achieved in the understanding of the phenomenon of complexity and its quantitative description." Mathematical Reviews"...focused on the formal description of complex systems...the authors discuss a great number of ideas developed in the field of complex systems and complexity....Those working on complexity theory will find this book an invaluable source since it offers a great number of stimulating ideas and guidance for future research." Journal of Statistical Physics"It is the definitive source for complexity in physical systems. Scientists and graduate students working or interested in this new field, especially physicists, mathematicians and theoretical computer scientists will find this book of value." Pageoph Synopsis:Very successful book in the Cambridge Nonlinear Science Series, now available in paperback. Synopsis:This is a comprehensive discussion of complexity as it arises in physical, chemical, and biological systems, as well as in mathematical models of nature. Common features of these apparently unrelated fields are emphasised and incorporated into a uniform mathematical description, with the support of a large number of detailed examples and illustrations. The uniformity of notation and the relegation of technical mathematical notions to the appendices will help the reader follow the main course of the discussion without much need for consulting standard textbooks or the original research papers. Table of ContentsPart I. Phenomenology and Models: 1. Introduction; 2. Examples of complex behaviour; 3. Mathematical models; Part II: 4. Symbolic representations of physical systems; 5. Probability, ergodic theory, and information; 6. Thermodynamic formalism; Part III. Formal Characterization of Complexity: 7. Physical and computational analysis of symbolic signals; 8. Algorithmic and grammatical complexities; 9. Hierarchical scaling complexities; 10. Summary and perspectives.
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