| Full text | |
| Author(s): |
Pessoa, Claudio
;
Ribeiro, Ronisio
;
Novaes, Douglas
;
Gouveia, Marcio
;
Euzebio, Rodrigo
Total Authors: 5
|
| Document type: | Journal article |
| Source: | NONLINEAR DYNAMICS; v. 111, n. 22, p. 23-pg., 2023-11-01. |
| Abstract | |
We obtain lower bounds for the maximum number of limit cycles bifurcating from periodic annuli of discontinuous planar piecewise linear Hamiltonian differential systems with three zones separated by two parallel straight lines, assuming that the linear differential subsystem in the region between the two straight lines, called of central subsystem, has a saddle at a point equidistant from these lines. (Obviously, the other subsystems have saddles or centers.) We prove that at least six limit cycles bifurcate from the periodic annuli of these kind of piecewise Hamiltonian differential systems, by linear perturbations. Normal forms and Melnikov functions, defined in two and three zones, are the main techniques used in the proof of the results. (AU) | |
| FAPESP's process: | 22/04040-6 - Dynamical properties of some classes of interval maps |
| Grantee: | Márcio Ricardo Alves Gouveia |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| 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: | 23/04061-6 - Continuous or piecewise smooth dynamical systems on 2 and 3 dimensional manifolds. |
| Grantee: | Cláudio Gomes Pessoa |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 22/09633-5 - Averaging theory for studying invariant tori and periodic behavior in differential equations and inclusions |
| Grantee: | Douglas Duarte Novaes |
| Support Opportunities: | Regular Research Grants |