Geodesic
The boundary of stability in a simple class of monodromic germs
Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 3, pp. 276-284

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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. 
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     author = {N. B. Medvedeva and V. A. Viktorova},
     title = {The boundary of  stability in a simple class of monodromic germs},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
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     publisher = {mathdoc},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_3_a2/}
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N. B. Medvedeva; V. A. Viktorova. The boundary of  stability in a simple class of monodromic germs. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 3, pp. 276-284. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_3_a2/