Advertisement

Deterministic Chaos in General Relativity

  • David Hobill
  • Adrian Burd
  • Alan Coley

Part of the NATO ASI Series book series (NSSB, volume 332)

Table of contents

  1. Front Matter
    Pages i-xi
  2. A Brief Review of “Deterministic Chaos in General Relativity”

  3. Mathematical Preliminaries

    1. Front Matter
      Pages 17-17
    2. John Wainwright
      Pages 19-61
    3. Richard C. Churchill
      Pages 63-88
    4. Richard Cushman
      Pages 89-101
    5. David L. Rod, Richard C. Churchill
      Pages 103-105
    6. Richard C. Churchill
      Pages 107-112
    7. P. T. Chruściel, J. Isenberg
      Pages 113-125
  4. Compact Relativistic Systems

    1. Front Matter
      Pages 127-127
    2. G. Contopoulos
      Pages 129-144
    3. M. W. Choptuik
      Pages 155-175
  5. Cosmological Systems

    1. Front Matter
      Pages 177-177
    2. M. A. H. MacCallum
      Pages 179-201
    3. Esteban Calzetta
      Pages 203-235
    4. George Ellis, Reza Tavakol
      Pages 237-250
    5. Marcelo B. Ribeiro
      Pages 269-296
    6. A. A. Coley, R. J. van den Hoogen
      Pages 297-306
    7. B. K. Berger, D. Garfinkle, V. Moncrief, C. M. Swift
      Pages 307-313
  6. Bianchi IX (Mixmaster) Dynamics

    1. Front Matter
      Pages 315-315
    2. Charles W. Misner
      Pages 317-328
    3. Gerson Francisco, George E. A. Matsas
      Pages 355-358
    4. G. Contopoulos, B. Grammaticos, A. Ramani
      Pages 423-432
  7. Back Matter
    Pages 463-472

About this book

Introduction

Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com­ plex nonlinear systems that cannot be broken down into the behavior of their con­ stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.

Keywords

chaos dynamical systems dynamische Systeme geometry numerical methods

Editors and affiliations

  • David Hobill
    • 1
  • Adrian Burd
    • 2
  • Alan Coley
    • 2
  1. 1.University of CalgaryCalgaryCanada
  2. 2.Dalhousie UniversityHalifaxCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-9993-4
  • Copyright Information Springer-Verlag US 1994
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-9995-8
  • Online ISBN 978-1-4757-9993-4
  • Series Print ISSN 0258-1221
  • Buy this book on publisher's site
Industry Sectors
Electronics
Aerospace
Oil, Gas & Geosciences