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 Chelyab. Fiz.-Mat. Zh., 2019, Volume 4, Issue 3, Pages 276–284 (Mi chfmj145)

Mathematics

The boundary of stability in a simple class of monodromic germs

N. B. Medvedeva, V. A. Viktorova

Chelyabinsk State University, Chelyabinsk, Russia

Abstract: A two-parameter family of vector fields is constructed with a monodromic singular point and with a Newton diagram consisting of one edge. For this family, the conditions of "nondegeneracy" are satisfied, allowing it to be assigned to a class with a simple monodromic singular point. The asymptotics of the stability boundary in this family is constructed, which contains terms with a logarithm, which implies the analytical unsolvability of the stability problem in the closure of this class of vector fields with a simple monodromic singular point.

Keywords: monodromic singular point, focus, center, monodromy transformation, Newton diagram, stability boundary, analytic solvability.

DOI: https://doi.org/10.24411/2500-0101-2019-14303

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UDC: 517.9
Revised: 09.09.2019

Citation: N. B. Medvedeva, V. A. Viktorova, “The boundary of stability in a simple class of monodromic germs”, Chelyab. Fiz.-Mat. Zh., 4:3 (2019), 276–284

Citation in format AMSBIB
\Bibitem{MedVik19} \by N.~B.~Medvedeva, V.~A.~Viktorova \paper The boundary of stability in a simple class of monodromic germs \jour Chelyab. Fiz.-Mat. Zh. \yr 2019 \vol 4 \issue 3 \pages 276--284 \mathnet{http://mi.mathnet.ru/chfmj145} \crossref{https://doi.org/10.24411/2500-0101-2019-14303}