2 citations · 5 across the 6 of their papers we have counts for
8 papers
Qualitative planar dynamics with star nodes and homogeneous nonlinearities: beyond Hilbert's problem
Begoña Alarcón, Sofia B. S. D. Castro, Isabel S. Labouriau
This is a full study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a homogeneous polynomial of arbi…
Global Saddles for Planar Maps
Begoña Alarcón, Sofia B. S. D. Castro, Isabel S. Labouriau
We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a glob…
Hopf bifurcation at infinity and dissipative vector fields of the plane
Begoña Alarcón, Roland Rabanal
We describe some families of differentiable vector fields with the Hopf bifurcation at infinity, without assuming the continuous differentiability. These vector fields have isolate…
Discrete Symmetric Planar Dynamics
B. Alarcón, S. B. S. D. Castro, I. S. Labouriau
We review previous results providing sufficient conditions to determine the global dynamics for equivariant maps of the plane with a unique fixed point which is also hyperbolic.
Global Dynamics for Symmetric Planar Maps
B. Alarcon, S. B. S. D. Castro, I. S. Labouriau
We consider sufficient conditions to determine the global dynamics for equivariant maps of the plane with a unique fixed point which is also hyperbolic. When the map is equivariant…
A local but not global attractor for a Zn-symmetric map
B. Alarcon, S. B. S. D. Castro, I. S. Labouriau
There are many tools for studying local dynamics. An important problem is how this information can be used to obtain global information. We present examples for which local stabili…