Work

Bruno Ideal and the Variety of Centers for Singular Germs of Vector Fields

Year: 2026

Type: article

Abstract: Given a germ of singular analytic vector field $$\partial $$ , we consider the locus where $$\partial $$ is formally equivalent to its linear part. In the logarithmic case, this locus is defined by the vanishing of a formal ideal $$B(\partial )$$ . We show that, under convenient arithmetic conditions on the linear part of $$\partial $$ , such ideal $$B(\partial )$$ is in fact analytic. As a consequence, its zero set V is an analytic invariant variety and the foliation defined by the restriction $$\partial |_V$$ is analytically linearizable.

Source: Qualitative Theory of Dynamical Systems

DOI: 10.1007/s12346-026-01614-w

Authors: María Martín-Vega, Daniel Panazzolo

Institutions: Centre National de la Recherche Scientifique, Universidad de Cantabria, Université Paris Cité, Sorbonne Université, Sorbonne Paris Cité

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: Agence Nationale de la Recherche, Ministerio de Ciencia e Innovación, Universidad de Valladolid, Agencia Estatal de Investigación