Surfaces with central configuration and Dulac's problem for a three dimensional isolated Hopf singularity
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914658698395648 |
|---|---|
| author | Corral, Nuria Vega, María Martín Sánchez, Fernando Sanz |
| author_facet | Corral, Nuria Vega, María Martín Sánchez, Fernando Sanz |
| contents | Let $ξ$ be a real analytic vector field with an elementary isolated singularity at $0\in \mathbb{R}^3$ and eigenvalues $\pm bi,c$ with $b,c\in \mathbb{R}$ and $b\neq 0$. We prove that all cycles of $ξ$ in a sufficiently small neighborhood of $0$, if they exist, are contained in a finite number of subanalytic invariant surfaces entirely composed by a continuum of cycles. In particular, we solve Dulac's problem, i.e. finiteness of limit cycles, for such vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Surfaces with central configuration and Dulac's problem for a three dimensional isolated Hopf singularity Corral, Nuria Vega, María Martín Sánchez, Fernando Sanz Dynamical Systems 34C05 (Primary) 34C08, 34C07, 34C20, 37C10, 37C25 (Secondary) Let $ξ$ be a real analytic vector field with an elementary isolated singularity at $0\in \mathbb{R}^3$ and eigenvalues $\pm bi,c$ with $b,c\in \mathbb{R}$ and $b\neq 0$. We prove that all cycles of $ξ$ in a sufficiently small neighborhood of $0$, if they exist, are contained in a finite number of subanalytic invariant surfaces entirely composed by a continuum of cycles. In particular, we solve Dulac's problem, i.e. finiteness of limit cycles, for such vector fields. |
| title | Surfaces with central configuration and Dulac's problem for a three dimensional isolated Hopf singularity |
| topic | Dynamical Systems 34C05 (Primary) 34C08, 34C07, 34C20, 37C10, 37C25 (Secondary) |
| url | https://arxiv.org/abs/2401.16484 |