Attractivity and Bifurcation for Nonautonomous Dynamical 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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Rasmussen, Martin (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
Σειρά:Lecture Notes in Mathematics, 1907
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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490 1 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 1907 
505 0 |a Notions of Attractivity and Bifurcation -- Nonautonomous Morse Decompositions -- LinearSystems -- Nonlinear Systems -- Bifurcations in Dimension One -- Bifurcations of Asymptotically Autonomous Systems. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Dynamics. 
650 0 |a Ergodic theory. 
650 0 |a Differential equations. 
650 1 4 |a Mathematics. 
650 2 4 |a Ordinary Differential Equations. 
650 2 4 |a Dynamical Systems and Ergodic Theory. 
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830 0 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 1907 
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