Center manifolds for smooth invariant manifolds. (English) Zbl 0953.34038
Summary: The authors study dynamics of flows generated by smooth vector fields in \({\mathbb{R}}^n\) in the vicinity of an invariant and closed smooth manifold \(Y\). By applying the Hadamard graph transform technique, they show that there exists an invariant manifold (called a center manifold of \(Y\)) based on the information of the linearization along \(Y\), which contains every locally bounded solution and is persistent under small perturbations.
MSC:
| 34C45 | Invariant manifolds for ordinary differential equations |
| 37D10 | Invariant manifold theory for dynamical systems |
| 34C30 | Manifolds of solutions of ODE (MSC2000) |
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