Giovanni Gallavotti Livres

Focusing on the properties of stationary states in chaotic systems, this book explores time-invariant distributions relevant to physics, drawing on historical analyses of foundational figures like Boltzmann, Clausius, and Maxwell. It emphasizes the "chaotic hypothesis," extending classical ergodic theory to non-equilibrium phenomena, and provides a fresh interpretation of SRB measures. The author links statistical mechanics with chaotic systems and presents current research, making it accessible for advanced students through heuristic proofs and detailed references, while maintaining a historical perspective.

Focusing on theoretical mechanics, this book presents foundational concepts without assuming extensive prior knowledge, requiring only basic classical physics and calculus. It emphasizes classical arguments while intentionally omitting modern formal developments and detailed analyses of specific problems like planetary motion and ergodic theory. The content reflects lectures given at the University of Rome from 1975 to 1978, aiming to provide a comprehensive yet concise exploration of essential mechanical principles.

The apparent contradiction of the results of the Fermi-Pasta-Ulam experiment conducted in 1953 and 1954 with the hypothesis that essentially any nonlinearity would lead to a system exhibiting ergodic behaviour has become known as the Fermi-Pasta-Ulam Problem. This volume reviews the current understanding of this paradox without trying to force coherence on differing perspectives on the same problem by various groups or approaches. The contributions comprise studies of one-dimensional chains, descriptions of numerical methods, heuristic theories, addressing the long standing and controversial problem of distinguishing chaos from noise in signal analysis, metastability, the relation of the FPU motions with the integrable equations, approaches using methods of perturbation theory and the proof of the applicability of KAM theory in FPU chains with energy very close to a minimum. For the convenience of the reader the original work of FPU is reprinted in an appendix. The order of the contributions reflects the aim of leading the interested but inexperienced reader through gradual understanding, starting from general analysis, and proceeding towards more specialized topics."

Intended for beginners in ergodic theory, this book addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e. g., Asonov systems or KAM Theory. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.

This monograph on fluid mechanics is not only a superb and unique textbook but also an impressive piece of research. It is the only textbook that fully covers turbulence, all the way from the works of Kolmogorov to modern dynamics.

The author is one of the leading scientists in mathematical physics and a well-known expert in statistical mechanics This work on the fundamental concepts is unparalleled in the literature Includes supplementary material: sn. pub/extras