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The Fermi-Pasta-Ulam Problem

A Status Report

  • Giovanni Gallavotti

Part of the Lecture Notes in Physics book series (LNP, volume 728)

Table of contents

  1. Front Matter
    Pages I-VII
  2. G. Gallavotti
    Pages 1-19
  3. Allan J. Lichtenberg, Roberto Livi, Marco Pettini, Stefano Ruffo
    Pages 21-121
  4. Massimo Cencini, Fabio Cecconi, Massimo Falcioni, Angelo Vulpiani
    Pages 123-149
  5. G. Benettin, A. Carati, L. Galgani, A. Giorgilli
    Pages 151-189
  6. Dario Bambusi, Antonio Ponno
    Pages 191-205
  7. Simone Paleari, Tiziano Penati
    Pages 239-282

About this book

Introduction

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.

Keywords

FPU experiment Integrable systems KdV equation Statistical Mechanics dynamical systems ergodic hypothesis

Editors and affiliations

  • Giovanni Gallavotti
    • 1
  1. 1.Dipartimento di MatematicaUniversità Roma La SapienzaPiazzale Aldo MoroItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-72995-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-72994-5
  • Online ISBN 978-3-540-72995-2
  • Series Print ISSN 0075-8450
  • Buy this book on publisher's site
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