A note on the convergence of parametrised non-resonant invariant manifolds. (English) Zbl 1209.37028
Summary: Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds.
MSC:
| 37D10 | Invariant manifold theory for dynamical systems |
| 34C45 | Invariant manifolds for ordinary differential equations |
| 34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |
| 37M99 | Approximation methods and numerical treatment of dynamical systems |
| 65G20 | Algorithms with automatic result verification |
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