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  • Textbook
  • © 1997

Chaos

An Introduction to Dynamical Systems

Authors:

  1. Kathleen T. Alligood

    1. George Mason University, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Tim D. Sauer

    1. George Mason University, USA

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    You can also search for this author in PubMed   Google Scholar

  3. James A. Yorke

    1. University of Maryland, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Textbooks in Mathematical Sciences (TIMS)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xvii
    PDF

  2. One-Dimensional Maps

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 1-42

  3. Two-Dimensional Maps

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 43-104

  4. Chaos

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 105-147

  5. Fractals

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 149-191

  6. Chaos in Two-Dimensional Maps

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 193-230

  7. Chaotic Attractors

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 231-271

  8. Differential Equations

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 273-327

  9. Periodic Orbits and Limit Sets

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 329-358

  10. Chaos in Differential Equations

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 359-397

  11. Stable Manifolds and Crises

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 399-445

  12. Bifurcations

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 447-498

  13. Cascades

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 499-536

  14. State Reconstruction from Data

    • Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
    Pages 537-556

  15. Back Matter

    Pages 557-603
    PDF
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About this book

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ­ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.
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Keywords

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Authors and Affiliations

  • George Mason University, USA

    Kathleen T. Alligood, Tim D. Sauer

  • University of Maryland, USA

    James A. Yorke

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Bibliographic Information

  • Book Title: Chaos

  • Book Subtitle: An Introduction to Dynamical Systems

  • Authors: Kathleen T. Alligood, Tim D. Sauer, James A. Yorke

  • Series Title: Textbooks in Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-642-59281-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • eBook ISBN: 978-3-642-59281-2Published: 06 December 2012

  • Series ISSN: 1431-9381

  • Edition Number: 1

  • Number of Pages: XVII, 603

  • Number of Illustrations: 285 b/w illustrations, 10 illustrations in colour

  • Topics: Analysis, Complex Systems, Statistical Physics and Dynamical Systems

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Buy it now

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

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