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.

UDC: 517.9

Received: 23.07.2019
Revised: 09.09.2019

DOI: 10.24411/2500-0101-2019-14303