Normal forms and transition map near a symmetric planar saddle connection [ Back ]

15:30 to 16:30
UAB - Dept. Matemàtiques (C1/-128)
Jeroen Wijnen
Universiteit Hasselt


We consider a heteroclinic connection in a planar system, between two symmetric hyperbolic saddles of which the eigenvalues are resonant. This situation typically appears in the local study of non-elementary singular points by means of a blow-up or after compactification of the phase space.

We start by providing a semi-local normal form containing the information of both saddles simultaneously using a procedure similar to the Poincaré-Dulac normalization. By means of an infinite set of finitely smooth functions, we further reduce this normal form to an easily integrable system providing us with a constant of motion of the system in normal form. Finally, we use this invariant to obtain an asymptotic expression for the transition map near the connection of the vector field in normal form.