| Full text | |
| Author(s): |
Gouveia, Luiz F. S.
;
Torregrosa, Joan
Total Authors: 2
|
| Document type: | Journal article |
| Source: | PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. N/A, p. 20-pg., 2022-04-19. |
| Abstract | |
In 1991, Chicone and Jacobs showed the equivalence between the computation of the first-order Taylor developments of the Lyapunov constants and the developments of the first Melnikov function near a non-degenerate monodromic equilibrium point, in the study of limit cycles of small-amplitude bifurcating from a quadratic centre. We show that their proof is also valid for polynomial vector fields of any degree. This equivalence is used to provide a new lower bound for the local cyclicity of degree six polynomial vector fields, so M(6) >= 44. Moreover, we extend this equivalence to the piecewise polynomial class. Finally, we prove that M-p(c)(4) >= 43 and M-p(c)(5) >= 65. (AU) | |
| FAPESP's process: | 20/04717-0 - Dynamical systems with symmetries and implicit differential equations |
| Grantee: | Luiz Fernando da Silva Gouveia |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |