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Record Nr. |
UNINA9910484101703321 |
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Autore |
Rasmussen Martin <1975-> |
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Titolo |
Attractivity and bifurcation for nonautonomous dynamical systems. / / Martin Rasmussen |
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Pubbl/distr/stampa |
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Berlin, Germany : , : Springer, , [2007] |
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©2007 |
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ISBN |
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1-280-90224-8 |
9786610902248 |
3-540-71225-9 |
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Edizione |
[1st ed. 2007.] |
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Descrizione fisica |
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1 online resource (221 p.) |
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Collana |
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Lecture notes in mathematics ; ; 1907 |
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Disciplina |
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Soggetti |
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Differential equations, Linear |
Differentiable dynamical systems |
Bifurcation theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Notions of Attractivity and Bifurcation -- Nonautonomous Morse Decompositions -- LinearSystems -- Nonlinear Systems -- Bifurcations in Dimension One -- Bifurcations of Asymptotically Autonomous Systems. |
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Sommario/riassunto |
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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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