Chaos and coarse graining in statistical mathematics

Massimo Falcioni, Annick Lesne, Angelo Vulpiani

"While statistical mechanics can describe the equilibrium state of systems with many degrees of freedom, and dynamical systems can explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed of a huge number of particles." "The first part of the book introduces the basic concepts of chaotic dynamics. The book then moves on to explore the role of ergodicity and chaos for the validity of statistical laws. The last part of the book is devoted to the treatment of problems characterized by the presence of more than one significant scale. In addition, the authors also discuss the relevance that many degrees of freedom, coarse graining procedure, and instability mechanisms, have in justifying a statistical...

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