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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

 

 

Analytic classification of saddle nodes


Authors: S. M. Voronin and Yu. I. Meshcheryakova
Translated by: G. G. Gould
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 66 (2005).
Journal: Trans. Moscow Math. Soc. 2005, 85-103
MSC (2000): Primary 82B44, 82C44, 60K35; Secondary 47N55, 47B80
Published electronically: November 9, 2005
MathSciNet review: 2193430
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Abstract | References | Similar Articles | Additional Information

Abstract: Isolated degenerate elementary singular points (saddle nodes) of germs of holomorphic vector fields in $ (\mathbb{C}^2,0)$ are studied. An analytic classification of them is obtained; it is shown that the analytic classification has two times more moduli (numeric and functional) than the orbital analytic classification. A theorem on sectorial normalization is proved.


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Additional Information

S. M. Voronin
Affiliation: Chernigov State University, Chernigov, Ukraine
Email: ivanlosev@yandex.ru

Yu. I. Meshcheryakova
Affiliation: Chernigov State University, Chernigov, Ukraine

DOI: https://doi.org/10.1090/S0077-1554-05-00151-2
Published electronically: November 9, 2005
Additional Notes: This work was carried out with the support of RFFI (Grant No. 03-01-00270), CDRF (Grant No. RM-1-2358-MO-02).
Article copyright: © Copyright 2005 American Mathematical Society