| Full text | |
| Author(s): |
Gouveia, Luiz F. S.
;
da Silva, Paulo R. R.
;
Rondon, Gabriel
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Qualitative Theory of Dynamical Systems; v. 22, n. 1, p. 26-pg., 2023-03-01. |
| 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 n(2) + 3n + 2 parameters, a polynomial holomorphic depends only on 2n +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 Poincar & eacute; 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 is an element of C. We also classify all the possible global phase portraits of Moebius systems z? = Az+B/ Cz+D , where A, B, C, D is an element of C, AD - BC &NOTEQUexpressionL; 0. (AU) | |
| FAPESP's process: | 20/06708-9 - Piecewise Holomorphic Systems and Regularization of Filippov fields around degenerated singularities and regular tangential polycycles |
| Grantee: | Gabriel Alexis Rondón Vielma |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| 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 |