Nonlinear Systems

Part of the Lecture Notes in Mathematics book series (LNM, volume 1907)

In the study of nonlinear systems, invariant manifolds play a central role, since they help to understand the often complicated dynamical behavior near an equilibrium, a periodic solution or—in the nonautonomous context—an arbitrary solution. The construction of stable and unstable invariant manifolds goes back to Poincaré [136] and Hadamard [73]. In the sequel, the theory was extended from hyperbolic to nonhyperbolic systems, from finite to infinite dimension and from time-independent to time-dependent equations.


Nonlinear System Trivial Solution Invariant Manifold Negative Real Part Invariant Projector 
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© Springer-Verlag Berlin Heidelberg 2007

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