2.
Cláudio Pessoa; Ronísio Ribeiro; Douglas D. Novaes; Márcio R. A. Gouveia; Rodrigo Euzébio
On cyclicity in discontinuous piecewise linear near-hamiltonian differential systems with three zones having a saddle in the central one Journal Article
Em: Nonlinear Dynamics, 2023.
@article{EuzGouNovPesRib2023,
title = {On cyclicity in discontinuous piecewise linear near-hamiltonian differential systems with three zones having a saddle in the central one},
author = {Cláudio Pessoa and Ronísio Ribeiro and Douglas D. Novaes and Márcio R. A. Gouveia and Rodrigo Euzébio},
url = {https://arxiv.org/abs/2212.00828},
year = {2023},
date = {2023-10-04},
urldate = {2022-12-16},
journal = {Nonlinear Dynamics},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
1.
Márcio R. A. Gouveia; Jaume Llibre; Douglas D. Novaes; Cláudio Pessoa
Piecewise smooth dynamical systems: persistenc of periodic solutions and normal forms Journal Article
Em: Journal of Differential Equations, vol. 260, pp. 6180-6129, 2016.
@article{GouLliNovPesJDE2015,
title = {Piecewise smooth dynamical systems: persistenc of periodic solutions and normal forms},
author = {Márcio R. A. Gouveia and Jaume Llibre and Douglas D. Novaes and Cláudio Pessoa},
url = {http://dx.doi.org/10.1016/j.jde.2015.12.034},
doi = {10.1016/j.jde.2015.12.034},
year = {2016},
date = {2016-04-05},
journal = {Journal of Differential Equations},
volume = {260},
pages = {6180-6129},
abstract = {We consider a n-dimensional piecewise smooth vector fields with two zones separated by a hyperplane S which admits an invariant hyperplane O transversal to S containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n=3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms.
},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We consider a n-dimensional piecewise smooth vector fields with two zones separated by a hyperplane S which admits an invariant hyperplane O transversal to S containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n=3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms.
