Analytic classification of saddle nodes
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S. M. Voronin and Yu. I. Meshcheryakova
Translated by: G. G. Gould - Trans. Moscow Math. Soc. 2005, 85-103
- DOI: https://doi.org/10.1090/S0077-1554-05-00151-2
- Published electronically: November 9, 2005
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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.References
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Bibliographic Information
- S. M. Voronin
- Affiliation: Chernigov State University, Chernigov, Ukraine
- Email: ivanlosev@yandex.ru
- Yu. I. Meshcheryakova
- Affiliation: Chernigov State University, Chernigov, Ukraine
- 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).
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2005, 85-103
- MSC (2000): Primary 82B44, 82C44, 60K35; Secondary 47N55, 47B80
- DOI: https://doi.org/10.1090/S0077-1554-05-00151-2
- MathSciNet review: 2193430