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Mathematical Structures of Nonlinear Science

An Introduction

  • Melvyn S. Berger

Part of the Nonlinear Topics in the Mathematical Sciences book series (NTMS, volume 1)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Melvyn S. Berger
    Pages 144-227
  3. Melvyn S. Berger
    Pages 294-347
  4. Melvyn S. Berger
    Pages 348-381
  5. Back Matter
    Pages 382-421

About this book

Introduction

This is the first volume of a series of books that will describe current advances and past accompli shments of mathemat i ca 1 aspects of nonlinear sCience taken in the broadest contexts. This subject has been studied for hundreds of years, yet it is the topic in whi ch a number of outstandi ng di scoveri es have been made in the past two decades. Clearly, this trend will continue. In fact, we believe some of the great scientific problems in this area will be clarified and perhaps resolved. One of the reasons for this development is the emerging new mathematical ideas of nonlinear science. It is clear that by looking at the mathematical structures themselves that underlie experiment and observation that new vistas of conceptual thinking lie at the foundation of the unexplored area in this field. To speak of specific examples, one notes that the whole area of bifurcation was rarely talked about in the early parts of this century, even though it was discussed mathematically by Poi ncare at the end of the ni neteenth century. I n another di rect ion, turbulence has been a key observation in fluid dynamics, yet it was only recently, in the past decade, that simple computer studies brought to light simple dynamical models in which chaotic dynamics, hopefully closely related to turbulence, can be observed.

Keywords

bifurcation calculus calculus of variations differential equation dynamical systems integrable system integration iteration manifold partial differential equation superconductivity vortices

Authors and affiliations

  • Melvyn S. Berger
    • 1
  1. 1.Department of MathematicsUniversity of MassachusettsAmherstUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-0579-5
  • Copyright Information Springer Science+Business Media B.V. 1990
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-6748-5
  • Online ISBN 978-94-009-0579-5
  • Series Print ISSN 0925-6660
  • Buy this book on publisher's site
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