Atlantis Studies in Dynamical Systems

Normally Hyperbolic Invariant Manifolds

The Noncompact Case

Authors: Eldering, Jaap

  • A gentle introduction: examples, history, overview of methods
  • Bridges nonlinear dynamics and differential geometry
  • ¬†Includes various new results in bounded geometry¬†
  • Completely worked out persistence proof using the Perron method
  • Multiple appendices with background material
see more benefits

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-94-6239-003-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-94-6239-002-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-94-6239-042-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

This monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems.
First, normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due to noncompactness are discussed in great detail with examples.
The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-known results by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompactness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed to analyze ODEs in a differential geometric context.
Finally, the main result is extended to time and parameter dependent systems and overflowing invariant manifolds.

Table of contents (4 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-94-6239-003-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-94-6239-002-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-94-6239-042-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Normally Hyperbolic Invariant Manifolds
Book Subtitle
The Noncompact Case
Authors
Series Title
Atlantis Studies in Dynamical Systems
Series Volume
2
Copyright
2013
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the author
eBook ISBN
978-94-6239-003-4
DOI
10.2991/978-94-6239-003-4
Hardcover ISBN
978-94-6239-002-7
Softcover ISBN
978-94-6239-042-3
Edition Number
1
Number of Pages
XII, 189
Topics