The boundary of stability in a simple class of monodromic germs
N. B. Medvedeva, V. A. Viktorova
Chelyabinsk State University, Chelyabinsk, Russia
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.
monodromic singular point, focus, center, monodromy transformation, Newton diagram, stability boundary, analytic solvability.
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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
\by N.~B.~Medvedeva, V.~A.~Viktorova
\paper The boundary of stability in a simple class of monodromic germs
\jour Chelyab. Fiz.-Mat. Zh.
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