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Attractivity and Bifurcation for Nonautonomous Dynamical Systems [electronic resource] / by Martin Rasmussen.

By: Contributor(s): Material type: TextTextSeries: Lecture Notes in Mathematics ; 1907Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: XI, 217 p. online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540712251
Subject(s): Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:
  • 515.352 23
LOC classification:
  • QA372
Online resources:
Contents:
Notions of Attractivity and Bifurcation -- Nonautonomous Morse Decompositions -- LinearSystems -- Nonlinear Systems -- Bifurcations in Dimension One -- Bifurcations of Asymptotically Autonomous Systems.
In: Springer eBooksSummary: 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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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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