Rigidity of saddle loops
Dynamical Systems
2025-11-21 v2
Abstract
A saddle loop is a germ of a holomorphic foliation near a homoclinic saddle connection. We prove that they are classied by their Poincar{\'e} rst-return map. We also prove that they are formally rigid when the Poincar{\'e} map is multivalued. Finally, we provide a list of all analytic classes of Liouville-integrable saddle loops.
Cite
@article{arxiv.2112.15058,
title = {Rigidity of saddle loops},
author = {Daniel Panazzolo and Maja Resman and Loïc Teyssier},
journal= {arXiv preprint arXiv:2112.15058},
year = {2025}
}