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RT Book, Whole SR Electronic DC OPAC T1 Attractivity and Bifurcation for Nonautonomous Dynamical Systems / by Martin Rasmussen T2 Lecture Notes in Mathematics A1 Rasmussen, Martin A1 SpringerLink (Online service) YR 2007 FD 2007 SP XI, 217 p K1 Mathematics K1 Dynamics K1 Ergodic theory K1 Differential equations K1 Mathematics K1 Ordinary Differential Equations K1 Dynamical Systems and Ergodic Theory PB Springer Berlin Heidelberg PP Berlin, Heidelberg SN 9783540712251 LA English (英語) CL DC23:515.352 NO 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 NO 書誌ID=1002178690; LK [E Book]http://dx.doi.org/10.1007/978-3-540-71225-1 OL 30