Nonlinear Systems

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.