# Separatrix skeleton in some 1-parameter families of planar vector fields

Date:
16.06.14
Times:
15:30 to 16:30
Place:
CRM - Auditori (C1/034)
Speaker:
Magdalena Caubergh
University:
Universitat Autònoma de Barcelona

#### Abstract:

In this talk we consider the 1-parameter family given by
$\dot{x} = y^3 - x^{2k+1}, \,\dot{y}= -x + m y^{4k+1},$
where $m$ is a real parameter and $k$ is an arbitrary but fixed integer with $k>0.$ We describe the dynamical mechanism underlying the bifurcation of separatrices in function of $m,$ and obtain the bifurcation diagram of the separatrix skeleton for this 1-parameter family.