Handbook of Dynamical Systems, Volume 3

1st Edition

Editors: H. Broer F. Takens B. Hasselblatt
Hardcover ISBN: 9780444531414
eBook ISBN: 9780080932262
Imprint: North Holland
Published Date: 12th October 2010
Page Count: 560
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Table of Contents

1. Introduction, 2. Complex linearization, 3. KAM Theory for circle and annulus maps, 4. KAM Theory for flows, 5. Further developments in KAM Theory, 6. Quasi-periodic bifurcations: dissipative setting, 7. Quasi-periodic bifurcation theory in other settings, 8. Further Hamiltonian KAM Theory, 9. Whitney smooth bundles of KAM tori, 10. Conclusion


Description

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.

Key Features

  • Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems
  • Highlights developments that are the foundation for future research in this field
  • Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Readership

This is a reference work for students and professionals working with Dynamical Systems.


Details

No. of pages:
560
Language:
English
Copyright:
© North Holland 2010
Published:
Imprint:
North Holland
eBook ISBN:
9780080932262
Hardcover ISBN:
9780444531414
Paperback ISBN:
9780444638212

Reviews

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.


About the Editors

H. Broer Editor

Affiliations and Expertise

University of Groningen, Department of Mathematics, Groningen, The Netherlands

F. Takens Editor

Affiliations and Expertise

University of Groningen, Department of Mathematics, Groningen, The Netherlands

B. Hasselblatt Editor

Affiliations and Expertise

Tufts University, Department of Mathematics, Medford, MA USA