Attractivity and Bifurcation for Nonautonomous Dynamical Systems [electronic resource] / by Martin Rasmussen.
Material type: TextSeries: Lecture Notes in Mathematics ; 1907Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: XI, 217 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540712251Subject(s): Mathematics | Differentiable dynamical systems | Differential Equations | Mathematics | Ordinary Differential Equations | Dynamical Systems and Ergodic TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 515.352 LOC classification: QA372Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1856 |
Notions of Attractivity and Bifurcation -- Nonautonomous Morse Decompositions -- LinearSystems -- Nonlinear Systems -- Bifurcations in Dimension One -- Bifurcations of Asymptotically Autonomous Systems.
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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