Bifurcações de campos vetoriais em duas zonas com simetria
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2017-11-28
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Universidade Federal de Goiás
Resumo
In this work we study reversible vector fields in two zones and equivariant vector fields
in two zones. Our main result is the classification of the symmetric singularities of
codimensions 0,1 and 2 of such vector fields.
More precisely, in the reversible case in R3, where the dimension of the fixed points
variety of the involution associated to the vector field is 2, we present all bifurcation
diagram of the codimensions 1 and 2 singularities, describing the changes in the behavior
of the symmetric singularities and tangents of the vector field with the transition manifold,
S, according to the variation of the bifucartion parameter. We also show the existence of
invariant cylinders and, in this case, doing small perturbations we determine invariant
manifolds that persisted and we determine the number of limit cycles that were born.
When the vector field defined on two zones is equivariant, the dynamic is enriched with
the emergence of the sliding vector field and we also do a local study and the classification
of singularities (and pseudo-singularities) of codimensions 0,1 and 2. We show the
existence of homoclinic sliding orbit and that it is a codimension one phenomenon.
Moreover, provided the symmetry we get a double Shilnikov sliding orbit.
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Citação
CASTRO, Ubirajara José Gama de. Bifurcações de campos vetoriais em duas zonas com simetria. 2017. 119 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2017.