We introduce an embedding of real or complex n-dimensional space K-n as an algebraic variety V which is determined by the action of a linear one-parameter group. Every analytic vector field on Kn corresponds to some embedded vector field on V. For a symmetric vector field this embedded vector field splits into a reduced system and a direct sum of non-autonomous linear systems. Examples and applications are mostly concerned with Poincare-Dulac normal forms. Embeddings provide a natural setting for perturbations of symmetric systems, in particular of systems in normal form up to some degree.
Embedding and splitting ordinary differential equations in normal form / G. Gaeta, S. Walcher. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 224:1(2006 May), pp. 98-119.
Embedding and splitting ordinary differential equations in normal form
G. GaetaPrimo
;
2006
Abstract
We introduce an embedding of real or complex n-dimensional space K-n as an algebraic variety V which is determined by the action of a linear one-parameter group. Every analytic vector field on Kn corresponds to some embedded vector field on V. For a symmetric vector field this embedded vector field splits into a reduced system and a direct sum of non-autonomous linear systems. Examples and applications are mostly concerned with Poincare-Dulac normal forms. Embeddings provide a natural setting for perturbations of symmetric systems, in particular of systems in normal form up to some degree.Pubblicazioni consigliate
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