Ronaldo A. Garcia and Marco A. Teixeira, A Boundary Cusp Singular Point and
Reversible Vector Fields on the Plane
Abstract:
In this paper we describe
the bifurcation diagram of a boundary cusp of codimension three, i.e, a
Bogdanov-Takens singular point in the boundary of the semi plane $\{(x,y)\in
{\mathbb R}^2:\; x\geq 0\}$. This study is applied to the analysis of the
behavior of singularity of the germ of vector field
$X_{0}(x,y)=(y,2x(x^4+x^2y))$ in the class of reversible vector fields. We
classify the generic three parameter families of reversible vector fields
$X_{a,b,c}$ with $(a,b,c) \in ({\mathbb R^3},0)$ and $X_{a,b,c}=X_0$.
Copy
of the file:
rp06-04.ps (postscript)
rp06-04.ps.gz (gzipped postscript)
February18, 2004