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Lecture Notes in Mathematics

Attractivity and Bifurcation for Nonautonomous Dynamical Systems

Authors: Rasmussen, Martin

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About this book

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.

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From the reviews:

"In this volume the reader will find a theory of breakdown of stability and a theory of transition for a one-parameter family of nonautonomous dynamical systems. … This book presents a wealth of interesting theoretical concepts, which will certainly be important in the further development of the theory of breakdown of stability and of transition for nonautonomous dynamical systems." (Russell A. Johnson, Mathematical Reviews, Issue 2008 k)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-540-71225-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-540-71224-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Attractivity and Bifurcation for Nonautonomous Dynamical Systems
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1907
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-71225-1
DOI
10.1007/978-3-540-71225-1
Softcover ISBN
978-3-540-71224-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XI, 217
Topics