On the cyclicity of persistent hyperbolic polycycles
Dynamical Systems
2025-12-16 v1
Abstract
In this work we consider families of smooth vector fields having a persistent polycycle with hyperbolic saddles. We derive the asymptotic expansion of the return map associated to the polycycle, determining explicitly its leading terms. As a consequence, explicit conditions on the leading terms allow us to determine the cyclicity of such polycycles. We then apply our results to study the cyclicity of a polycycle of a model with applications in Game Theory.
Cite
@article{arxiv.2504.07225,
title = {On the cyclicity of persistent hyperbolic polycycles},
author = {Lucas Queiroz Arakaki and Paulo Santana},
journal= {arXiv preprint arXiv:2504.07225},
year = {2025}
}