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Table of contents (7 chapters)
Keywords
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.
Reviews
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)
Authors and Affiliations
Bibliographic Information
Book Title: Attractivity and Bifurcation for Nonautonomous Dynamical Systems
Authors: Martin Rasmussen
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-71225-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2007
Softcover ISBN: 978-3-540-71224-4Published: 08 June 2007
eBook ISBN: 978-3-540-71225-1Published: 26 May 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XI, 217
Topics: Ordinary Differential Equations, Dynamical Systems and Ergodic Theory