Complexity: Hierarchical Structures and Scaling in Physics
This is a comprehensive discussion of complexity as it arises in physical, chemical and biological systems, as well as in mathematical models of nature. The aim of this book is to illustrate the ways in which complexity manifests itself and to introduce a sequence of increasingly sharp mathematical methods for the classification of complex behavior. This book will be of interest to graduate students and researchers in physics (nonlinear dynamics, fluid dynamics, solid-state, cellular...
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Very successful book in the Cambridge Nonlinear Science Series, now available in paperback.
PrefacePt. 1Phenomenology and models1Ch. 1Introduction3Ch. 2Examples of complex behaviour12Ch. 3Mathematical models32Pt. 2Mathematical tools67Ch. 4Symbolic representations of physical systems69Ch. 5Probability, ergodic theory, and information85Ch. 6Thermodynamic formalism119Pt. 3Formal characterization of complexity163Ch. 7Physical and computational analysis of symbolic signals165Ch. 8Algorithmic and grammatical complexities213Ch. 9Hierarchical scaling complexities248Ch. 10Summary and perspectives277App. 1The Lorenz model281App. 2The horseshoe map283App. 3Mathematical definitions285App. 4Lyapunov exponents, entropy, and dimension287App. 5Forbidden words in regular languages290References293Index311
