Monodromic Nilpotent Singular Points with Odd Andreev Number and the Center Problem

• Autor(a) principal: Pessoa, Claudio [UNESP]
• Data de Publicação: 2022
• Outros Autores: Queiroz, Lucas [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s12346-022-00638-2; http://hdl.handle.net/11449/237645
• topic: Monodromy; Nilpotent singular points; Center Problem

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.