Regular and Chaotic Dynamics

  • A. J. Lichtenberg
  • M. A. Lieberman

Part of the Applied Mathematical Sciences book series (AMS, volume 38)

Table of contents

  1. Front Matter
    Pages i-xv
  2. A. J. Lichtenberg, M. A. Lieberman
    Pages 1-69
  3. A. J. Lichtenberg, M. A. Lieberman
    Pages 70-161
  4. A. J. Lichtenberg, M. A. Lieberman
    Pages 162-244
  5. A. J. Lichtenberg, M. A. Lieberman
    Pages 245-292
  6. A. J. Lichtenberg, M. A. Lieberman
    Pages 293-372
  7. A. J. Lichtenberg, M. A. Lieberman
    Pages 373-456
  8. A. J. Lichtenberg, M. A. Lieberman
    Pages 457-569
  9. A. J. Lichtenberg, M. A. Lieberman
    Pages 570-643
  10. Back Matter
    Pages 644-693

About this book

Introduction

What's in a name? The original title of our book, Regular and Stochastic Motion, was chosen to emphasize Hamiltonian dynamics and the physical motion of bodies. The new edition is more evenhanded, with considerably more discussion of dissipative systems and dynamics not involving physical motion. To reflect this partial change of emphasis, we have substituted the more general terms in our title. The common usage of the new terms clarifies the emphasis of the book. The main change in the book has been to expand the sections on dissipative dynamics, including discussion of renormalization, circle maps, intermittancy, crises, transient chaos, multifractals, reconstruction, and coupled mapping systems. These topics were either mainly in the mathemati­ cal literature or essentially unstudied when our first edition was written. The volume of work in these areas has surpassed that in Hamiltonian dynamics within the past few years. We have also made changes in the Hamiltonian sections, adding many new topics such as more general transformation and stability theory, connected stochasticity in two-dimensional maps, converse KAM theory, new topics in diffusion theory, and an approach to equilibrium in many dimensions. Other sections such as mapping models have been revised to take into account new perspectives. We have also corrected a number of misprints and clarified various arguments with the help of colleagues and students, some of whom we acknowledge below. We have again chosen not to treat quantum chaos, partly due to our own lack ofacquaintance with the subject.

Keywords

Hamiltonsche Bewegungsgleichungen Motion Nichtlineare Schwingung Stochastischer Prozess Störung (Math.) differential equation

Authors and affiliations

  • A. J. Lichtenberg
    • 1
  • M. A. Lieberman
    • 1
  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2184-3
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3100-9
  • Online ISBN 978-1-4757-2184-3
  • Series Print ISSN 0066-5452
  • About this book
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