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Table of contents

  1. Front Matter
    Pages i-xiii
  2. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 1-18
  3. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 19-124
  4. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 125-166
  5. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 167-200
  6. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 201-228
  7. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 229-268
  8. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 269-314
  9. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 315-346
  10. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 347-370
  11. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 371-390
  12. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 391-406
  13. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 407-432
  14. Eric J. Kostelich
    Pages 433-442
  15. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 443-458
  16. Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 459-466
  17. Back Matter
    Pages 467-485

About this book

Introduction

Plotting trajectories is a useful capability in exploring a dynamical system, but it is just the beginning. The Maryland Chaos Group developed an array of tools to help visualize the properties of dynamical systems induding automatic method for plotting all "basins and attractors " , and for automatically searching for all computing "straddle trajectories", periodic orbits of a specified period. In the investigations of the Maryland Chaos Group, I. A. Yorke found it useful to be able to combine these various basic tools with each other into so that each new study could benefit a single package that grew with time from the previous programming efforts. He has been writing this software and distributing versions for the last nine years. The resulting program Dynamics requires either a Unix workstation running XII graphics or an IBM PC compatible computer. Eric I. Kostelich has put in a great deal of effort to port the program to Unix workstations. Some basic tools in Dynamics, such as the computation of Lyapunov exponents and the use of Newton's method are standard. The method of computation of stable and unstable manifolds is superior to standard procedures. Dynamics is currently being used extensively in our research and it is being used in undergraduate courses. Dynamics: Numerical Explora#ons provides an introduction to and overview of fundamental tools and numerical methods together with many simple examples. All the numerical methods described in this book are implemented in Dynamics.

Keywords

chaos differential equation dynamical systems numerical method

Authors and affiliations

  • Helena E. Nusse
    • 1
    • 2
  • James A. Yorke
    • 2
  • Eric J. Kostelich
    • 3
  1. 1.Vakgroep EconometrieRijksuniversiteit GroningenGroningenThe Netherlands
  2. 2.Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA
  3. 3.Department of MathematicsArizona State UniversityTempeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0231-5
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94334-3
  • Online ISBN 978-1-4684-0231-5
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site