Attractivity and Bifurcation for Nonautonomous Dynamical Systems

2007
ISBN: 978-3-540-71224-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1907, 217 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 359 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Rasmussen, Martin

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

Notions of Attractivity and Bifurcation.- Nonautonomous Morse Decompositions.- LinearSystems.- Nonlinear Systems.- Bifurcations in Dimension One.- Bifurcations of Asymptotically Autonomous Systems.