Artículos de revistas
Monodromic Nilpotent Singular Points with Odd Andreev Number and the Center Problem
Fecha
2022-12-01Registro en:
Qualitative Theory Of Dynamical Systems. Basel: Springer Basel Ag, v. 21, n. 4, 24 p., 2022.
1575-5460
10.1007/s12346-022-00638-2
WOS:000834818300001
Autor
Universidade Estadual Paulista (UNESP)
Institución
Resumen
Given a nilpotent singular point of a planar vector field, its monodromy is associated with its Andreev number n. The parity of n determines whether the existence of an inverse integrating factor implies that the singular point is a nilpotent center. For n odd, this is not always true. We give a characterization for a family of systems having Andreev number n such that the center problem cannot be solved by the inverse integrating factor method. Moreover, we study general properties of this family, determining necessary center conditions for every n and solving the center problem in the case n = 3.