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The analytic and formal normal form for the nilpotent singularity. The case of generalized saddle-node. (English) Zbl 1027.34099
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 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 M. Berthier, R. Meziani and P. Sad [Bull. Sci. Math. 123, 351–370 (1999; Zbl 0963.32021)].

34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
Full Text: DOI
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