The local cyclicity problem: Melnikov method using Lyapunov constants
| dc.contributor.author | Gouveia, Luiz F. S. [UNESP] | |
| dc.contributor.author | Torregrosa, Joan | |
| dc.contributor.institution | Universitat Autònoma de Barcelona | |
| dc.contributor.institution | Universidade Estadual Paulista (UNESP) | |
| dc.contributor.institution | Centre de Recerca Matemàtica | |
| dc.date.accessioned | 2023-03-01T19:55:25Z | |
| dc.date.available | 2023-03-01T19:55:25Z | |
| dc.date.issued | 2022-05-19 | |
| dc.description.abstract | In 1991, Chicone and Jacobs showed the equivalence between the computation of the firstorder 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, soM(6) ≥ 44. Moreover, we extend this equivalence to the piecewise polynomial class. Finally, we prove that Mcp(4) ≥ 43 and Mcp(5) ≥ 65. | en |
| dc.description.affiliation | Departament de Matemàtiques Universitat Autònoma de Barcelona, Bellaterra | |
| dc.description.affiliation | Departamento de Matemática Universidade Estadual Paulista | |
| dc.description.affiliation | Centre de Recerca Matemàtica, Campus de Bellaterra, Bellaterra | |
| dc.description.affiliationUnesp | Departamento de Matemática Universidade Estadual Paulista | |
| dc.format.extent | 356-375 | |
| dc.identifier | http://dx.doi.org/10.1017/S0013091522000128 | |
| dc.identifier.citation | Proceedings of the Edinburgh Mathematical Society, v. 65, n. 2, p. 356-375, 2022. | |
| dc.identifier.doi | 10.1017/S0013091522000128 | |
| dc.identifier.issn | 1464-3839 | |
| dc.identifier.issn | 0013-0915 | |
| dc.identifier.scopus | 2-s2.0-85129202595 | |
| dc.identifier.uri | http://hdl.handle.net/11449/239965 | |
| dc.language.iso | eng | |
| dc.relation.ispartof | Proceedings of the Edinburgh Mathematical Society | |
| dc.source | Scopus | |
| dc.subject | local cyclicity | |
| dc.subject | Lyapunov constants | |
| dc.subject | Melnikov theory | |
| dc.title | The local cyclicity problem: Melnikov method using Lyapunov constants | en |
| dc.type | Artigo | |
| unesp.author.orcid | 0000-0003-2919-6724 0000-0003-2919-6724[1] | |
| unesp.author.orcid | 0000-0002-2753-1827 0000-0002-2753-1827[2] |