Work

Surfaces with Central Configuration and Dulac’s Problem for a Three Dimensional Isolated Hopf Singularity

Year: 2024

Type: article

Abstract: Let $$\xi $$ ξ be a real analytic vector field with an elementary isolated singularity at $$0\in \mathbb {R}^3$$ 0 ∈ R 3 and eigenvalues $$\pm bi,c$$ ± b i , c with $$b,c\in \mathbb {R}$$ b , c ∈ R and $$b\ne 0$$ b ≠ 0 . We prove that all cycles of $$\xi $$ ξ in a sufficiently small neighborhood of 0, if they exist, are contained in the union of finitely many subanalytic invariant surfaces, each one entirely composed of a continuum of cycles. In particular, we solve Dulac’s problem for such vector fields, i.e., finiteness of limit cycles.

Source: Journal of Dynamics and Differential Equations

DOI: 10.1007/s10884-024-10377-4

Authors: Nuria Corral, María Martín-Vega, Fernando Sanz Sánchez

Institutions: Universidad de Cantabria, Universidad de Valladolid

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: $2,990