The analytic and formal normal form for the nilpotent singularity. The case of generalized saddle-node
type: Item
instance of: scholarly article
title: The analytic and formal normal form for the nilpotent singularity. The case of generalized saddle-node
zbMATH Open document ID: 1027.34099
DOI: 10.1016/S0007-4497(02)01127-2
author: Ewa Stróżyna
published in: Bulletin des Sciences Mathématiques
publication date: 2003-03-23T00:00:00Z
review text: The generalized saddle-node case of certain vector fields is considered. The aim is to provide analogous results to those of the same author and \textit{H. Żolądek} [J. Differ. Equations 179, 479--537 (2002; Zbl 1005.34034)], and of other authors cited in the current paper, in the generalized cusp case. It is shown that two germs of analytic vector fields (with generalized saddle-node singularity) are analytically equivalent if and only if their monodromy groups are analytically equivalent. The proof makes use of a restricted version of the same theorem due to \textit{M. Berthier, R. Meziani} and \textit{P. Sad} [Bull. Sci. Math. 123, 351--370 (1999; Zbl 0963.32021)].
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 34M55
zbMATH DE Number: 1886866
zbMATH Keywords: nilpotent singularities of vector fields
zbMATH Keywords: orbital equivalence
zbMATH Keywords: normal form
zbMATH Keywords: monodromy group
reviewed by: Andrew Pickering
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1886866