Global Phase Portrait and Local Integrability of Holomorphic Systems
| dc.contributor.author | Gouveia, Luiz F. S. [UNESP] | |
| dc.contributor.author | da Silva, Paulo R. [UNESP] | |
| dc.contributor.author | Rondón, Gabriel [UNESP] | |
| dc.contributor.institution | Universidade Estadual Paulista (UNESP) | |
| dc.date.accessioned | 2023-07-29T13:38:19Z | |
| dc.date.available | 2023-07-29T13:38:19Z | |
| dc.date.issued | 2023-03-01 | |
| dc.description.abstract | Planar holomorphic systems x˙ = u(x, y) , y˙ = v(x, y) are those that u= Re (f) and v= Im (f) for some holomorphic function f(z). They have important dynamical properties, highlighting, for example, the fact that they do not have limit cycles and that center-focus problem is trivial. In particular, the hypothesis that a polynomial system is holomorphic reduces the number of parameters of the system. Although a polynomial system of degree n depends on n2+ 3 n+ 2 parameters, a polynomial holomorphic depends only on 2 n+ 2 parameters. In this work, in addition to prove that holomorphic systems are locally integrable, we classify all the possible global phase portraits, on the Poincaré disk, of systems z˙ = f(z) and z˙ = 1 / f(z) , where f(z) is a polynomial of degree 2, 3 and 4 in the variable z∈ C. We also classify all the possible global phase portraits of Moebius systems z˙=Az+BCz+D, where A, B, C, D∈ C, AD- BC≠ 0. | en |
| dc.description.affiliation | Departamento de Matemática - Instituto de Biociências Letras e Ciências Exatas UNESP - Universidade Estadual Paulista, Rua C. Colombo, 2265, São Paulo | |
| dc.description.affiliationUnesp | Departamento de Matemática - Instituto de Biociências Letras e Ciências Exatas UNESP - Universidade Estadual Paulista, Rua C. Colombo, 2265, São Paulo | |
| dc.identifier | http://dx.doi.org/10.1007/s12346-022-00734-3 | |
| dc.identifier.citation | Qualitative Theory of Dynamical Systems, v. 22, n. 1, 2023. | |
| dc.identifier.doi | 10.1007/s12346-022-00734-3 | |
| dc.identifier.issn | 1662-3592 | |
| dc.identifier.issn | 1575-5460 | |
| dc.identifier.scopus | 2-s2.0-85146636700 | |
| dc.identifier.uri | http://hdl.handle.net/11449/248237 | |
| dc.language.iso | eng | |
| dc.relation.ispartof | Qualitative Theory of Dynamical Systems | |
| dc.source | Scopus | |
| dc.title | Global Phase Portrait and Local Integrability of Holomorphic Systems | en |
| dc.type | Artigo |