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Mathematics and Its Applications

Shadowing in Dynamical Systems

Theory and Applications

Authors: Palmer, K.J.

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eBook $129.00
price for USA in USD (gross)
  • ISBN 978-1-4757-3210-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-7923-6179-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA in USD
  • ISBN 978-1-4419-4827-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic.
It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic.
Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.

Table of contents (11 chapters)

  • Hyperbolic Fixed Points of Diffeomorphisms and Their Stable and Unstable Manifolds

    Palmer, Ken

    Pages 1-20

  • Hyperbolic Sets of Diffeomorphisms

    Palmer, Ken

    Pages 21-55

  • Transversal Homoclinic Points of Diffeomorphisms and Hyperbolic Sets

    Palmer, Ken

    Pages 57-76

  • The Shadowing Theorem for Hyperbolic Sets of Diffeomorphisms

    Palmer, Ken

    Pages 77-90

  • Symbolic Dynamics Near a Transversal Homoclinic Point of a Diffeomorphism

    Palmer, Ken

    Pages 91-97

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-1-4757-3210-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-7923-6179-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA in USD
  • ISBN 978-1-4419-4827-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Shadowing in Dynamical Systems
Book Subtitle
Theory and Applications
Authors
Series Title
Mathematics and Its Applications
Series Volume
501
Copyright
2000
Publisher
Springer US
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4757-3210-8
DOI
10.1007/978-1-4757-3210-8
Hardcover ISBN
978-0-7923-6179-4
Softcover ISBN
978-1-4419-4827-4
Edition Number
1
Number of Pages
XIV, 300
Topics