Bruno Ideal and the Variety of Centers for Singular Germs of Vector Fields
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.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Mathematical Dynamics and Fractals
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Qualitative Theory of Dynamical Systems
- Volume
- 25
- Issue
- 6
- Publication date
- 16 October 2026
- Language
- EN