Sign up or sign in
logo
  1. Topology and Dynamics
  2. Icon: chevron
  3. SumTopo
  4. Icon: chevron
  5. 2026

Qualitative Theory and Bifurcations in Dynamics

Icon: calendar QTBD Session Talk #6.1 | 2026 Jul 16 from 03:15PM to 03:40PM (Zagreb) | B3-37 (Sibe Mardešić Hall)

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.