Subevent of QTBD Session #6
‟Normal forms for planar homoclinic 1:1 saddle loops” by joint with Maja Resman
Abstract:
We solve the embedding problem for Poincaré maps appearing in foliations on abstract complex surfaces near 1-polycycles corresponding to homoclinic connections of a 1:1 saddle point. We particularly prove that every such foliation is biholomorphic to a foliated neighborhood of some unique model saddle-loop in $\mathbb{C}^{2}$, defined in a neighborhood of an explicit singular elliptic curve.