6533b85efe1ef96bd12bfa93
RESEARCH PRODUCT
On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
Robert Roussariesubject
SeparatrixGeneral MathematicsSaddle pointMathematical analysisPerturbation (astronomy)Planar vector fieldsAtomic physicsMathematicsdescription
Consider a fami ly of vector fCelds x~ on the plane. This fami ly depends on a parameter ~ ~ /R A, for some A ~ /~, and is supposed to be 0 ~ in (m,~) 6 /i~ 2X /~A. Suppose that for ~ = O, the vector f i e l d X o has a separatrix loop. This means that X o has an hyperbol ic saddle point s o and that one of the stable separatr ix of 8 o coincides with one of the unstable one. The union of th is curve and s o is the loop ?. A return map is defined on one side of r .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1986-09-01 | Boletim da Sociedade Brasileira de Matemática |