Peixoto's Theorem for vector fields on $\mathbb{S}^2$ with impasse points [ Back ]

Date:
20.10.14   
Times:
15:30 to 16:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
João Carlos da Rocha Medrado
University:
Universidade Federal de Goiás

Abstract:

The structural stability of vector fields with impasse regular curves on $\mathbb{S}^2$ is studied and a version of the Peixoto's Theorem is established.

Moreover a global analysis of normal forms of the constrained systems $Ax.x' = F(x)$, $x \in \mathbb{R}^3$, $A\in M(3)$ and $F : \mathbb {R}^3 \rightarrow \mathbb{R}^3$ in the Poicaré ball (i.e. in the compactification of $\mathbb {R}^3$ with the sphere $\mathbb {S}^2$ of the infinity) is made.

The talk is based on a joint work with Claudio Buzzi and Paulo Ricardo da Silva.