A formal series approach to the center manifold theorem - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Foundations of Computational Mathematics Year : 2018

A formal series approach to the center manifold theorem


This paper considers near-equilibrium systems of ordinary differential equations with explicit separation of the slow and stable manifolds. Formal B-series like those previously used to analyze highly-oscillatory systems or to construct modified equations are employed here to construct expansions of the change of variables, the center invariant manifold and the reduced model. The new approach may be seen as a process of reduction to a normal form, with the main advantage, as compared to the standard view conveyed by the celebrated center manifold theorem, that it is possible to recover the complete solution at any time through an explicit change of variables.
Fichier principal
Vignette du fichier
V12.pdf (1.5 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01279715 , version 1 (26-02-2016)
hal-01279715 , version 2 (15-04-2016)



François Castella, Philippe Chartier, Julie Sauzeau. A formal series approach to the center manifold theorem. Foundations of Computational Mathematics, 2018, 18 (6), pp.1397-1434. ⟨10.1007/s10208-017-9371-y⟩. ⟨hal-01279715v2⟩
299 View
706 Download



Gmail Facebook X LinkedIn More