Attractivity and Bifurcation for Nonautonomous Dynamical Systems
Rasmussen, Martin.
Attractivity and Bifurcation for Nonautonomous Dynamical Systems [electronic resource] / by Martin Rasmussen. - XI, 217 p. online resource. - Lecture Notes in Mathematics, 1907 0075-8434 ; . - Lecture Notes in Mathematics, 1907 .
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.
9783540712251
10.1007/978-3-540-71225-1 doi
Differential Equations.
Differentiable dynamical systems.
Ordinary Differential Equations.
Dynamical Systems and Ergodic Theory.
QA372
515.352
Attractivity and Bifurcation for Nonautonomous Dynamical Systems [electronic resource] / by Martin Rasmussen. - XI, 217 p. online resource. - Lecture Notes in Mathematics, 1907 0075-8434 ; . - Lecture Notes in Mathematics, 1907 .
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.
9783540712251
10.1007/978-3-540-71225-1 doi
Differential Equations.
Differentiable dynamical systems.
Ordinary Differential Equations.
Dynamical Systems and Ergodic Theory.
QA372
515.352